Showing 1–50 of 51 results for author: Neri, I

Metastable phase separation and information retrieval in multicomponent mixtures

Authors: Rodrigo Braz Teixeira, Davide Marcato, Izaak Neri, Pablo Sartori

Abstract: Liquid mixtures can separate into phases with distinct composition. This phenomenon has recently come back to prominence due to its role in complex biological liquids, such as the cytoplasm, which contain thousands of components. For simple two-component mixtures phase-separated states are global free energy minima. However, local free energy minima, i.e. metastable states, are known to play a dom… ▽ More Liquid mixtures can separate into phases with distinct composition. This phenomenon has recently come back to prominence due to its role in complex biological liquids, such as the cytoplasm, which contain thousands of components. For simple two-component mixtures phase-separated states are global free energy minima. However, local free energy minima, i.e. metastable states, are known to play a dominant role in complex systems with many components. For example, Hopfield neural networks can retrieve information from partial cues via relaxation to metastable states. Under what conditions can phase separated states be metastable, and what are the implications for information processing in multicomponent liquids? In this work we develop the general thermodynamic formalism of metastable phase separation. We then apply this formalism to an illustrative toy example inspired by recent experiments, binary mixtures with high-order interactions. Finally, as core application of the formalism, we study metastability in Hopfield liquids, a class of multicomponent mixtures capable of storing information on the composition of phases. We show that these phases can be retrieved from partial cues via metastable phase separation. Spatial simulations of liquids with a large number of components match our analytical solution. Our work suggests that complex biological mixtures can perform information retrieval through metastable phase separation. △ Less

Submitted 18 June, 2026; v1 submitted 12 September, 2025; originally announced September 2025.

Comments: 26 pages, 8 figures, 16 pages of supplement

Eigenvalue spectral tails and localization properties of asymmetric networks

Authors: Pietro Valigi, Joseph W. Baron, Izaak Neri, Giulio Biroli, Chiara Cammarota

Abstract: In contrast to the neatly bounded spectra of densely populated large random matrices, sparse random matrices often exhibit unbounded eigenvalue tails on the real and imaginary axis, called Lifshitz tails. In the case of asymmetric matrices, concise mathematical results have proved elusive. In this work, we present an analytical approach to characterising these tails. We exploit the fact that eigen… ▽ More In contrast to the neatly bounded spectra of densely populated large random matrices, sparse random matrices often exhibit unbounded eigenvalue tails on the real and imaginary axis, called Lifshitz tails. In the case of asymmetric matrices, concise mathematical results have proved elusive. In this work, we present an analytical approach to characterising these tails. We exploit the fact that eigenvalues in the tail region have corresponding eigenvectors that are exponentially localised on highly-connected hubs of the network associated to the random matrix. We approximate these eigenvectors using a series expansion in the inverse connectivity of the hub, where successive terms in the series take into account further sets of next-nearest neighbours. By considering the ensemble of such hubs, we are able to characterise the eigenvalue density and the extent of localisation in the tails of the spectrum in a general fashion. As such, we classify a number of different asymptotic behaviours in the Lifshitz tails, as well as the leading eigenvalue and the inverse participation ratio. We demonstrate how an interplay between matrix asymmetry, network structure, and the edge-weight distribution leads to the variety of observed behaviours. △ Less

Submitted 5 November, 2025; v1 submitted 27 July, 2025; originally announced July 2025.

Comments: 37 pages and 10 figures in main text, 36 pages and 2 figure in supplemental material

Journal ref: Pietro Valigi et al 2025 J. Phys. A: Math. Theor. 58 455002

Thermodynamic bounds and symmetries in first-passage problems of fluctuating currents

Authors: Adarsh Raghu, Izaak Neri

Abstract: We develop a method for deriving thermodynamic bounds for first-passage problems of currents with two boundaries in Markov chains. Using this method, we derive a thermodynamic bound on the rate of dissipation in terms of the splitting probability and the first-passage time statistics of a fluctuating current, which is a refinement of a previously derived inequality. We also show that the concept o… ▽ More We develop a method for deriving thermodynamic bounds for first-passage problems of currents with two boundaries in Markov chains. Using this method, we derive a thermodynamic bound on the rate of dissipation in terms of the splitting probability and the first-passage time statistics of a fluctuating current, which is a refinement of a previously derived inequality. We also show that the concept of effective affinity, originally developed for continuous-time Markov chains, naturally extends to discrete-time Markov chains. Furthermore, we analyse symmetries in first-passage problems of fluctuating currents with two boundaries. We show that optimal currents -- those for which the effective affinity fully accounts for the dissipation -- satisfy a symmetry property: the current's average speed to reach the positive threshold equals the current's speed to reach the negative threshold. The developed approach uses a coarse-graining procedure for the average entropy production at random times and uses martingale methods to perform time-reversal of first-passage quantities. △ Less

Submitted 29 June, 2026; v1 submitted 4 July, 2025; originally announced July 2025.

Comments: 55 pages, 8 figures, typos corrected in Eqs. (27), (38), (76), (77), (90), (91), and (160)

Journal ref: New J. Phys. 27, 124602 (2025)

Thermodynamic Cost of Random-Time Protocols

Authors: Izaak Neri

Abstract: Systems that are driven by a randomly timed, external protocol can seemingly violate the second law of thermodynamics. We show that this thermodynamic paradox is resolved if the outcome of the random time is stored in a memory device. Specifically, we show that the average work required to erase the memory is at least as large as the average work gained from the protocol. We also discuss concrete… ▽ More Systems that are driven by a randomly timed, external protocol can seemingly violate the second law of thermodynamics. We show that this thermodynamic paradox is resolved if the outcome of the random time is stored in a memory device. Specifically, we show that the average work required to erase the memory is at least as large as the average work gained from the protocol. We also discuss concrete setups that measure random times directly without continuous monitoring. Taken together, this paper discusses the relationship between temporal information and thermodynamics. This framework is relevant for external protocols employing random times, such as stochastic resetting protocols and cyclically driven heat engines that use randomly timed protocols. △ Less

Submitted 13 August, 2026; v1 submitted 8 June, 2025; originally announced June 2025.

Comments: 15 pages, 9 figures, the new version fixed some typos

Journal ref: Phys. Rev. E 112, 044114 (2025)

Martingale approach for first-passage problems of time-additive observables in Markov processes

Authors: Izaak Neri

Abstract: We develop a method based on martingales to study first-passage problems of time-additive observables exiting an interval of finite width in a Markov process. In the limit that the interval width is large, we derive generic expressions for the splitting probability and the cumulants of the first-passage time. These expressions relate first-passage quantities to the large deviation properties of th… ▽ More We develop a method based on martingales to study first-passage problems of time-additive observables exiting an interval of finite width in a Markov process. In the limit that the interval width is large, we derive generic expressions for the splitting probability and the cumulants of the first-passage time. These expressions relate first-passage quantities to the large deviation properties of the time-additive observable. We find that there are three qualitatively different regimes depending on the properties of the large deviation rate function of the time-additive observable. These regimes correspond to exponential, super-exponential, or sub-exponential suppression of events at the unlikely boundary of the interval. Furthermore, we show that the statistics of first-passage times at both interval boundaries are in general different, even for symmetric thresholds and in the limit of large interval widths. While the statistics of the times to reach the likely boundary are determined by the cumulants of the time-additive observables in the original process, those at the unlikely boundary are determined by a dual process. We obtain these results from a one-parameter family of positive martingales that we call Perron martingales, as these are related to the Perron root of a tilted version of the transition rate matrix defining the Markov process. Furthermore, we show that each eigenpair of the tilted matrix has a one-parameter family of martingales. To solve first-passage problems at finite thresholds, we generally require all one-parameter families of martingales, including the non-positive ones. We illustrate this by solving the first-passage problem for run-and-tumble particles exiting an interval of finite width. △ Less

Submitted 13 August, 2026; v1 submitted 4 April, 2025; originally announced April 2025.

Comments: 45 pages, 6 figures. This version corrects a few typos, and corrects Eq. (131)

Journal ref: J. Phys. A: Math. Theor. 58, 145002 (2025)

Effective Affinity for Generic Currents in Markov Processes

Authors: Adarsh Raghu, Izaak Neri

Abstract: In nonequilibrium systems with uncoupled currents, the thermodynamic affinity determines the direction of currents, quantifies dissipation, and constrains current fluctuations. However, these properties of the thermodynamic affinity do not hold in complex systems with multiple coupled currents. For this reason, there has been an ongoing search in nonequilibrium thermodynamics for an affinity-like… ▽ More In nonequilibrium systems with uncoupled currents, the thermodynamic affinity determines the direction of currents, quantifies dissipation, and constrains current fluctuations. However, these properties of the thermodynamic affinity do not hold in complex systems with multiple coupled currents. For this reason, there has been an ongoing search in nonequilibrium thermodynamics for an affinity-like quantity, known as the effective affinity, which applies to a single current in a system with multiple coupled currents. Here, we introduce an effective affinity that applies to generic currents in time-homogeneous Markov processes. We show that the effective affinity is a single number encapsulating several dissipative and fluctuation properties of fluctuating currents: the effective affinity determines the direction of flow of the current; the effective affinity multiplied by the current is a lower bound for the rate of dissipation; for systems with uncoupled currents the effective affinity equals the standard thermodynamic affinity; and the effective affinity constrains negative fluctuations of currents, namely, it is the exponential decay constant of the distribution of current infima. We derive the above properties with large deviation theory and martingale theory, and one particular interesting finding is a class of martingales associated with generic currents. Furthermore, we make a study of the relation between effective affinities and stalling forces in a biomechanical model of motor proteins, and we find that both quantities are approximately equal when this particular model is thermodynamically consistent. This brings interesting perspectives on the use of stalling forces for the estimation of dissipation. △ Less

Submitted 9 April, 2025; v1 submitted 13 June, 2024; originally announced June 2024.

Comments: 46 Pages, 6 figures. Typo in Eqs. (10) and (12) corrected

Journal ref: J Stat Phys 192, 50 (2025)

Methods and Conversations in (Post)Modern Thermodynamics

Authors: Francesco Avanzini, Massimo Bilancioni, Vasco Cavina, Sara Dal Cengio, Massimiliano Esposito, Gianmaria Falasco, Danilo Forastiere, Nahuel Freitas, Alberto Garilli, Pedro E. Harunari, Vivien Lecomte, Alexandre Lazarescu, Shesha G. Marehalli Srinivas, Charles Moslonka, Izaak Neri, Emanuele Penocchio, William D. Piñeros, Matteo Polettini, Adarsh Raghu, Paul Raux, Ken Sekimoto, Ariane Soret

Abstract: Lecture notes after the doctoral school (Post)Modern Thermodynamics held at the University of Luxembourg, December 2022, 5-7, covering and advancing continuous-time Markov chains, network theory, stochastic thermodynamics, large deviations, deterministic and stochastic chemical reaction networks, metastability, martingales, quantum thermodynamics, and foundational issues. Lecture notes after the doctoral school (Post)Modern Thermodynamics held at the University of Luxembourg, December 2022, 5-7, covering and advancing continuous-time Markov chains, network theory, stochastic thermodynamics, large deviations, deterministic and stochastic chemical reaction networks, metastability, martingales, quantum thermodynamics, and foundational issues. △ Less

Submitted 19 January, 2024; v1 submitted 2 November, 2023; originally announced November 2023.

Comments: Submission to SciPost

Journal ref: SciPost Phys. Lect. Notes 80 (2024)

Liquid Hopfield model: retrieval and localization in multicomponent liquid mixtures

Authors: Rodrigo Braz Teixeira, Giorgio Carugno, Izaak Neri, Pablo Sartori

Abstract: Biological mixtures, such as the cellular cytoplasm, are composed of a large number of different components. From this heterogeneity, ordered mesoscopic structures emerge, such as liquid phases with controlled composition. These structures compete with each other for the same components. This raises several questions, such as what types of interactions allow the retrieval of multiple ordered mesos… ▽ More Biological mixtures, such as the cellular cytoplasm, are composed of a large number of different components. From this heterogeneity, ordered mesoscopic structures emerge, such as liquid phases with controlled composition. These structures compete with each other for the same components. This raises several questions, such as what types of interactions allow the retrieval of multiple ordered mesoscopic structures, and what are the physical limitations for the retrieval of said structures. In this work, we develop an analytically tractable model for liquids capable of retrieving states with target compositions. We name this model the liquid Hopfield model in reference to corresponding work in the theory of associative neural networks. By solving this model, we show that non-linear repulsive interactions are necessary for retrieval of target structures. We demonstrate that this is because liquid mixtures at low temperatures tend to transition to phases with few components, a phenomenon that we term localization. Taken together, our results demonstrate a trade-off between retrieval and localization phenomena in liquid mixtures. △ Less

Submitted 2 December, 2024; v1 submitted 28 October, 2023; originally announced October 2023.

Journal ref: Proc. Natl. Acad. Sci. U.S.A. 121 (48) e2320504121, (2024)

Local sign stability and its implications for spectra of sparse random graphs and stability of ecosystems

Authors: Pietro Valigi, Izaak Neri, Chiara Cammarota

Abstract: We study the spectral properties of sparse random graphs with different topologies and type of interactions, and their implications on the stability of complex systems, with particular attention to ecosystems. Specifically, we focus on the behaviour of the leading eigenvalue in different type of random matrices (including interaction matrices and Jacobian-like matrices), relevant for the assessmen… ▽ More We study the spectral properties of sparse random graphs with different topologies and type of interactions, and their implications on the stability of complex systems, with particular attention to ecosystems. Specifically, we focus on the behaviour of the leading eigenvalue in different type of random matrices (including interaction matrices and Jacobian-like matrices), relevant for the assessment of different types of dynamical stability. By comparing the results on Erdos-Renyi and Husimi graphs with sign-antisymmetric interactions or mixed sign patterns, we introduce a sufficient criterion, called strong local sign stability, for stability not to be affected by system size, as traditionally implied by the complexity-stability trade-off in conventional models of random matrices. The criterion requires sign-antisymmetric or unidirectional interactions and a local structure of the graph such that the number of cycles of finite length do not increase with the system size. Note that the last requirement is stronger than the classical local tree-like condition, which we associate to the less stringent definition of local sign stability, also defined in the paper. In addition, for strong local sign stable graphs which show stability to linear perturbations irrespectively of system size, we observe that the leading eigenvalue can undergo a transition from being real to acquiring a nonnull imaginary part, which implies a dynamical transition from nonoscillatory to oscillatory linear response to perturbations. Lastly, we ascertain the discontinuous nature of this transition. △ Less

Submitted 27 October, 2023; v1 submitted 17 March, 2023; originally announced March 2023.

Comments: 55 pages, 17 figures

Journal ref: J. Phys. Complex. 5, 015017 (2024)

Martingales for physicists: A treatise on stochastic thermodynamics and beyond

Authors: Édgar Roldán, Izaak Neri, Raphael Chetrite, Shamik Gupta, Simone Pigolotti, Frank Jülicher, Ken Sekimoto

Abstract: We review the theory of martingales as applied to stochastic thermodynamics and stochastic processes in physics more generally. We review the theory of martingales as applied to stochastic thermodynamics and stochastic processes in physics more generally. △ Less

Submitted 19 December, 2023; v1 submitted 18 October, 2022; originally announced October 2022.

Comments: 324 pages, 68 figures, submitted to Advances in Physics

Journal ref: Advances in Physics 72, 1-258 (2023)

Multicyclic norias: a first-transition approach to extreme values of the currents

Authors: Matteo Polettini, Izaak Neri

Abstract: For continuous-time Markov chains we prove that, depending on the notion of effective affinity $F$, the probability of an edge current to ever become negative is either $1$ if $F< 0$ else $\sim \exp - F$. The result generalizes a ``noria'' formula to multicyclic networks. We give operational insights on the effective affinity and compare several estimators, arguing that stopping problems may be mo… ▽ More For continuous-time Markov chains we prove that, depending on the notion of effective affinity $F$, the probability of an edge current to ever become negative is either $1$ if $F< 0$ else $\sim \exp - F$. The result generalizes a ``noria'' formula to multicyclic networks. We give operational insights on the effective affinity and compare several estimators, arguing that stopping problems may be more accurate in assessing the nonequilibrium nature of a system according to a local observer. Finally we elaborate on the similarity with the Boltzmann formula. The results are based on a constructive first-transition approach. △ Less

Submitted 7 November, 2023; v1 submitted 4 August, 2022; originally announced August 2022.

Comments: 25 pages, 2 figures

Journal ref: J Stat Phys 191, 35 (2024)

Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation

Authors: Izaak Neri, Matteo Polettini

Abstract: The infimum of an integrated current is its extreme value against the direction of its average flow. Using martingale theory, we show that the infima of integrated edge currents in time-homogeneous Markov jump processes are geometrically distributed, with a mean value determined by the effective affinity measured by a marginal observer that only sees the integrated edge current. In addition, we sh… ▽ More The infimum of an integrated current is its extreme value against the direction of its average flow. Using martingale theory, we show that the infima of integrated edge currents in time-homogeneous Markov jump processes are geometrically distributed, with a mean value determined by the effective affinity measured by a marginal observer that only sees the integrated edge current. In addition, we show that a marginal observer can estimate a finite fraction of the average entropy production rate in the underlying nonequilibrium process from the extreme value statistics in the integrated edge current. The estimated average rate of dissipation obtained in this way equals the above mentioned effective affinity times the average edge current. Moreover, we show that estimates of dissipation based on extreme value statistics can be significantly more accurate than those based on thermodynamic uncertainty ratios, as well as those based on a naive estimator obtained by neglecting nonMarkovian correlations in the Kullback-Leibler divergence of the trajectories of the integrated edge current. △ Less

Submitted 6 April, 2023; v1 submitted 4 August, 2022; originally announced August 2022.

Comments: 38 pages, 6 figures

Journal ref: SciPost Phys. 14, 131 (2023)

Estimating Entropy Production Rates with First-Passage Processes

Authors: Izaak Neri

Abstract: We consider the problem of estimating the mean entropy production rate in a nonequilibrium process from the measurements of first-passage quantities associated with a single current. For first-passage processes with large thresholds, Refs. [1, 2] identified a ratio of first-passage observables - involving the mean first-passage time, the splitting probability, and the first-passage thresholds - th… ▽ More We consider the problem of estimating the mean entropy production rate in a nonequilibrium process from the measurements of first-passage quantities associated with a single current. For first-passage processes with large thresholds, Refs. [1, 2] identified a ratio of first-passage observables - involving the mean first-passage time, the splitting probability, and the first-passage thresholds - that lower bounds the entropy production rate and is an unbiased estimator of the entropy production rate when applied to a current that is proportional to the stochastic entropy production. Here, we show that also at finite thresholds, a finite number of realisations of the nonequilibrium process, and for currents that are not proportional to the stochastic entropy production, first-passage ratios can accurately estimate the rate of dissipation. In particular, first-passage ratios capture a finite fraction of the total entropy production rate in regimes far from thermal equilibrium where thermodynamic uncertainty ratios capture a negligible fraction of the total entropy production rate. Moreover, we show that first-passage ratios incorporate nonMarkovian statistics in the estimated value of the dissipation rate, which are difficult to include in estimates based on Kullback-Leibler divergences. Taken together, we show that entropy production estimation with first-passage ratios is complementary to estimation methods based on thermodynamic uncertainty ratios and Kullback-Leibler divergences. △ Less

Submitted 13 August, 2026; v1 submitted 14 July, 2022; originally announced July 2022.

Comments: 32 pages, 7 figures, typos have been corrected in the new version

Journal ref: J. Phys. A: Math. Theor. 55, 304005 (2022)

Antagonistic interactions can stabilise fixed points in heterogeneous linear dynamical systems

Authors: Samuel Cure, Izaak Neri

Abstract: We analyse the stability of large, linear dynamical systems of variables that interact through a fully connected random matrix and have inhomogeneous growth rates. We show that in the absence of correlations between the coupling strengths, a system with interactions is always less stable than a system without interactions. Contrarily to the uncorrelated case, interactions that are antagonistic, i.… ▽ More We analyse the stability of large, linear dynamical systems of variables that interact through a fully connected random matrix and have inhomogeneous growth rates. We show that in the absence of correlations between the coupling strengths, a system with interactions is always less stable than a system without interactions. Contrarily to the uncorrelated case, interactions that are antagonistic, i.e., characterised by negative correlations, can stabilise linear dynamical systems. In particular, when the strength of the interactions is not too strong, systems with antagonistic interactions are more stable than systems without interactions. These results are obtained with an exact theory for the spectral properties of fully connected random matrices with diagonal disorder. △ Less

Submitted 25 December, 2025; v1 submitted 26 December, 2021; originally announced December 2021.

Comments: 31 pages, 7 figures, last version contains some corrections in Appendix F, typo corrected in the last term of (16)

Journal ref: SciPost Phys. 14, 093 (2023)

Instabilities of complex fluids with partially structured and partially random interactions

Authors: Giorgio Carugno, Izaak Neri, Pierpaolo Vivo

Abstract: We develop a theory for thermodynamic instabilities of complex fluids composed of many interacting chemical species organised in families. This model includes partially structured and partially random interactions and can be solved exactly using tools from random matrix theory. The model exhibits three kinds of fluid instabilities: one in which the species form a condensate with a local density th… ▽ More We develop a theory for thermodynamic instabilities of complex fluids composed of many interacting chemical species organised in families. This model includes partially structured and partially random interactions and can be solved exactly using tools from random matrix theory. The model exhibits three kinds of fluid instabilities: one in which the species form a condensate with a local density that depends on their family (family condensation); one in which species demix in two phases depending on their family (family demixing); and one in which species demix in a random manner irrespective of their family (random demixing). We determine the critical spinodal density of the three types of instabilities and find that the critical spinodal density is finite for both family condensation and family demixing, while for random demixing the critical spinodal density grows as the square root of the number of species. We use the developed framework to describe phase-separation instability of the cytoplasm induced by a change in pH. △ Less

Submitted 21 February, 2022; v1 submitted 7 September, 2021; originally announced September 2021.

Comments: 30 pages, 9 figures, Appendix included

Journal ref: Phys. Biol. 19, 056001 (2022)

Universal tradeoff relation between speed, uncertainty, and dissipation in nonequilibrium stationary states

Authors: Izaak Neri

Abstract: We derive universal thermodynamic inequalities that bound from below the moments of first-passage times of stochastic currents in nonequilibrium stationary states of Markov jump processes in the limit where the thresholds that define the first-passage problem are large. These inequalities describe a tradeoff between speed, uncertainty, and dissipation in nonequilibrium processes, which are quantif… ▽ More We derive universal thermodynamic inequalities that bound from below the moments of first-passage times of stochastic currents in nonequilibrium stationary states of Markov jump processes in the limit where the thresholds that define the first-passage problem are large. These inequalities describe a tradeoff between speed, uncertainty, and dissipation in nonequilibrium processes, which are quantified, respectively, with the moments of the first-passage times of stochastic currents, the splitting probability, and the mean entropy production rate. Near equilibrium, the inequalities imply that mean first-passage times are lower bounded by the Van't Hoff-Arrhenius law, whereas far from thermal equilibrium the bounds describe a universal speed limit for rate processes. When the current is the stochastic entropy production, then the bounds are equalities, a remarkable property that follows from the fact that the exponentiated negative entropy production is a martingale. △ Less

Submitted 14 August, 2026; v1 submitted 27 March, 2021; originally announced March 2021.

Comments: 50 pages, 6 figures. This version corrects a number of typographical errors in the published manuscript, including some in the equations of the appendices. The main results are unaffected

Journal ref: SciPost Phys. 12, 139 (2022)

Modelling the effect of ribosome mobility on the rate of protein synthesis

Authors: Olivier Dauloudet, Izaak Neri, Jean-Charles Walter, Jérôme Dorignac, Frédéric Geniet, Andrea Parmeggiani

Abstract: Translation is one of the main steps in the synthesis of proteins. It consists of ribosomes that translate sequences of nucleotides encoded on mRNA into polypeptide sequences of amino acids. Ribosomes bound to mRNA move unidirectionally, while unbound ribosomes diffuse in the cytoplasm. It has been hypothesized that finite diffusion of ribosomes plays an important role in ribosome recycling and th… ▽ More Translation is one of the main steps in the synthesis of proteins. It consists of ribosomes that translate sequences of nucleotides encoded on mRNA into polypeptide sequences of amino acids. Ribosomes bound to mRNA move unidirectionally, while unbound ribosomes diffuse in the cytoplasm. It has been hypothesized that finite diffusion of ribosomes plays an important role in ribosome recycling and that mRNA circularization enhances the efficiency of translation. In order to estimate the effect of cytoplasmic diffusion on the rate of translation, we consider a Totally Asymmetric Simple Exclusion Process (TASEP) coupled to a finite diffusive reservoir, which we call the Ribosome Transport model with Diffusion (RTD). In this model, we derive an analytical expression for the rate of protein synthesis as a function of the diffusion constant of ribosomes, which is corroborated with results from continuous-time Monte Carlo simulations. Using a wide range of biological relevant parameters, we conclude that diffusion in biological cells is fast enough so that it does not play a role in controlling the rate of translation initiation. △ Less

Submitted 17 January, 2022; v1 submitted 30 September, 2020; originally announced September 2020.

Comments: article, 16 pages, 5 figures

Journal ref: Eur. Phys. J. E 44, 19 (2021)

Dynamical systems on large networks with predator-prey interactions are stable and exhibit oscillations

Authors: Andrea Marcello Mambuca, Chiara Cammarota, Izaak Neri

Abstract: We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined on complex networks, such as, ecosystems consisting of a large number of species that interact through a food-web. We develop an exact theory for the spectral… ▽ More We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined on complex networks, such as, ecosystems consisting of a large number of species that interact through a food-web. We develop an exact theory for the spectral distribution and the leading eigenvalue of the corresponding sparse Jacobian matrices. This theory reveals that the nature of local interactions have a strong influence on system's stability. We show that, in general, linear dynamical systems defined on random graphs with a prescribed degree distribution of unbounded support are unstable if they are large enough, implying a tradeoff between stability and diversity. Remarkably, in contrast to the generic case, antagonistic systems that only contain interactions of the predator-prey type can be stable in the infinite size limit. This qualitatively feature for antagonistic systems is accompanied by a peculiar oscillatory behaviour of the dynamical response of the system after a perturbation, when the mean degree of the graph is small enough. Moreover, for antagonistic systems we also find that there exist a dynamical phase transition and critical mean degree above which the response becomes non-oscillatory. △ Less

Submitted 29 January, 2025; v1 submitted 23 September, 2020; originally announced September 2020.

Comments: 38 pages, 18 figures, last version fixes a typo in Eqs.(G11) and (G12)

Journal ref: Phys. Rev. E 105, 014305 (2022)

Localization and universality of eigenvectors in directed random graphs

Authors: Fernando L. Metz, Izaak Neri

Abstract: Although the spectral properties of random graphs have been a long-standing focus of network theory, the properties of right eigenvectors of directed graphs have so far eluded an exact analytic treatment. We present a general theory for the statistics of the right eigenvector components in directed random graphs with a prescribed degree distribution and with randomly weighted links. We obtain exac… ▽ More Although the spectral properties of random graphs have been a long-standing focus of network theory, the properties of right eigenvectors of directed graphs have so far eluded an exact analytic treatment. We present a general theory for the statistics of the right eigenvector components in directed random graphs with a prescribed degree distribution and with randomly weighted links. We obtain exact analytic expressions for the inverse participation ratio and show that right eigenvectors of directed random graphs with a small average degree are localized. Remarkably, if the fourth moment of the degree distribution is finite, then the critical mean degree of the localization transition is independent of the degree fluctuations, which is different from localization in undirected graphs that is governed by degree fluctuations. We also show that in the high connectivity limit the distribution of the right eigenvector components is solely determined by the degree fluctuations. For delocalized eigenvectors, we recover the universal results from standard random matrix theory that are independent of the degree distribution, while for localized eigenvectors the eigenvector distribution depends on the degree distribution. △ Less

Submitted 10 March, 2021; v1 submitted 27 July, 2020; originally announced July 2020.

Comments: 7 pages, 4 figures, 25 pages Supplemental Material

Journal ref: Phys. Rev. Lett. 126, 040604 (2021)

Second law of thermodynamics at stopping times

Authors: Izaak Neri

Abstract: Events in mesoscopic systems often take place at first-passage times, as is for instance the case for a colloidal particle that escapes a metastable state. An interesting question is how much work an external agent has done on a particle when it escapes a metastable state. We develop a thermodynamic theory for processes in mesoscopic systems that terminate at stopping times, which generalize first… ▽ More Events in mesoscopic systems often take place at first-passage times, as is for instance the case for a colloidal particle that escapes a metastable state. An interesting question is how much work an external agent has done on a particle when it escapes a metastable state. We develop a thermodynamic theory for processes in mesoscopic systems that terminate at stopping times, which generalize first-passage times. This theory implies a thermodynamic bound, reminiscent of the second law of thermodynamics, for the work exerted by an external protocol on a mesoscopic system at a stopping time. As an illustration, we use this law to bound the work required to stretch a polymer to a certain length or to let a particle escape from a metastable state. △ Less

Submitted 14 August, 2026; v1 submitted 4 February, 2020; originally announced February 2020.

Comments: 14 pages, 4 figures, the new version fixes some minor typographical errors

Journal ref: Phys. Rev. Lett. 124, 040601 (2020)

Linear stability analysis for large dynamical systems on directed random graphs

Authors: Izaak Neri, Fernando Lucas Metz

Abstract: We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such dynamical systems: First, infinitely large systems on directed graphs can be stable even when the degree distribution has unbounded support; this result is sur… ▽ More We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such dynamical systems: First, infinitely large systems on directed graphs can be stable even when the degree distribution has unbounded support; this result is surprising since their counterparts on nondirected graphs are unstable when system size is large enough. Second, we show that the phase transition between the stable and unstable phase is universal in the sense that it depends only on a few parameters, such as, the mean degree and a degree correlation coefficient. In addition, in the unstable regime we characterize the nature of the destabilizing mode, which also exhibits universal features. These results follow from an exact theory for the leading eigenvalue of infinitely large graphs that are locally tree-like and oriented, as well as, for the right and left eigenvectors associated with the leading eigenvalue. We corroborate analytical results for infinitely large graphs with numerical experiments on random graphs of finite size. We discuss how the presented theory can be extended to graphs with diagonal disorder and to graphs that contain nondirected links. Finally, we discuss the influence of small cycles and how they can destabilize large dynamical systems when they induce strong enough feedback loops. △ Less

Submitted 3 July, 2026; v1 submitted 19 August, 2019; originally announced August 2019.

Comments: Typo's have been corrected in the equations (C3), (C8) and(C9), and the caption of Figure 5. The original manuscript also interchanged sOut for sIn, and conversely, which affects Eqs.(56), (60), (D10), (H1), and (H4)

Journal ref: Phys. Rev. Research 2, 033313 (2020)

Universal transient behavior in large dynamical systems on networks

Authors: Wojciech Tarnowski, Izaak Neri, Pierpaolo Vivo

Abstract: We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient response of a system through the evolution in time of the squared norm of the state vector, which is averaged over different realizations of the initial perturbation… ▽ More We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient response of a system through the evolution in time of the squared norm of the state vector, which is averaged over different realizations of the initial perturbation. We develop a mathematical formalism that computes this quantity for graphs that are locally tree-like. We show that for unidirectional networks the theory simplifies and general analytical results can be derived. For example, we derive analytical expressions for the average squared norm for random directed graphs with a prescribed degree distribution. These analytical results reveal that unidirectional systems exhibit a high degree of universality in the sense that the average squared norm only depends on a single parameter encoding the average interaction strength between the individual constituents. In addition, we derive analytical expressions for the average squared norm for unidirectional systems with fixed diagonal disorder and with bimodal diagonal disorder. We illustrate these results with numerical experiments on large random graphs and on real-world networks. △ Less

Submitted 14 January, 2024; v1 submitted 14 June, 2019; originally announced June 2019.

Comments: 19 pages, 7 figures. We corrected a sign typo in the new version of the paper

Journal ref: Phys. Rev. Research 2, 023333 (2020)

Integral Fluctuation Relations for Entropy Production at Stopping Times

Authors: Izaak Neri, Edgar Roldán, Simone Pigolotti, Frank Jülicher

Abstract: A stopping time $T$ is the first time when a trajectory of a stochastic process satisfies a specific criterion. In this paper, we use martingale theory to derive the integral fluctuation relation $\langle e^{-S_{\rm tot}(T)}\rangle=1$ for the stochastic entropy production $S_{\rm tot}$ in a stationary physical system at stochastic stopping times $T$. This fluctuation relation implies the law… ▽ More A stopping time $T$ is the first time when a trajectory of a stochastic process satisfies a specific criterion. In this paper, we use martingale theory to derive the integral fluctuation relation $\langle e^{-S_{\rm tot}(T)}\rangle=1$ for the stochastic entropy production $S_{\rm tot}$ in a stationary physical system at stochastic stopping times $T$. This fluctuation relation implies the law $\langle S_{\rm tot}(T)\rangle\geq 0$, which states that it is not possible to reduce entropy on average, even by stopping a stochastic process at a stopping time, and which we call the second law of thermodynamics at stopping times. This law implies bounds on the average amount of heat and work a system can extract from its environment when stopped at a random time. Furthermore, the integral fluctuation relation implies that certain fluctuations of entropy production are universal or are bounded by universal functions. These universal properties descend from the integral fluctuation relation by selecting appropriate stopping times: for example, when $T$ is a first-passage time for entropy production, then we obtain a bound on the statistics of negative records of entropy production. We illustrate these results on simple models of nonequilibrium systems described by Langevin equations and reveal two interesting phenomena. First, we demonstrate that isothermal mesoscopic systems can extract on average heat from their environment when stopped at a cleverly chosen moment and the second law at stopping times provides a bound on the average extracted heat. Second, we demonstrate that the average efficiency at stopping times of an autonomous stochastic heat engines, such as Feymann's ratchet, can be larger than the Carnot efficiency and the second law of thermodynamics at stopping times provides a bound on the average efficiency at stopping times. △ Less

Submitted 11 September, 2019; v1 submitted 19 March, 2019; originally announced March 2019.

Comments: 37 pages, 6 figures

Journal ref: J. Stat. Mech. (2019) 104006

Spectral Theory of Sparse Non-Hermitian Random Matrices

Authors: Fernando Lucas Metz, Izaak Neri, Tim Rogers

Abstract: Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these matrices provide crucial information on system stability and susceptibility, however, their study is greatly complicated by the twin challenges of a lack of symmetry… ▽ More Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these matrices provide crucial information on system stability and susceptibility, however, their study is greatly complicated by the twin challenges of a lack of symmetry and a sparse interaction structure. In this review we provide a concise and systematic introduction to the main tools and results in this field. We show how the spectra of sparse non-Hermitian matrices can be computed via an analogy with infinite dimensional operators obeying certain recursion relations. With reference to three illustrative examples -- adjacency matrices of regular oriented graphs, adjacency matrices of oriented Erdős-Rényi graphs, and adjacency matrices of weighted oriented Erdős-Rényi graphs -- we demonstrate the use of these methods to obtain both analytic and numerical results for the spectrum, the spectral distribution, the location of outlier eigenvalues, and the statistical properties of eigenvectors. △ Less

Submitted 20 February, 2024; v1 submitted 26 November, 2018; originally announced November 2018.

Comments: 60 pages, 10 figures

Journal ref: 2019 J. Phys. A: Math. Theor. 52 434003

Martingale theory for housekeeping heat

Authors: Raphael Chetrite, Shamik Gupta, Izaak Neri, Édgar Roldán

Abstract: The housekeeping heat is the energy exchanged between a system and its environment in a nonequilibrium process that results from the violation of detailed balance. We describe fluctuations of the housekeeping heat in mesoscopic systems using the theory of martingales, a mathematical framework widely used in probability theory and finance. We show that the exponentiated housekeeping heat (in units… ▽ More The housekeeping heat is the energy exchanged between a system and its environment in a nonequilibrium process that results from the violation of detailed balance. We describe fluctuations of the housekeeping heat in mesoscopic systems using the theory of martingales, a mathematical framework widely used in probability theory and finance. We show that the exponentiated housekeeping heat (in units of $k_{\rm B}T$, with $k_{\rm B}$ the Boltzmann constant and $T$ the temperature) of a Markovian nonequilibrium process under arbitrary time-dependent driving is a martingale process. From this result, we derive universal equalities and inequalities for the statistics of stopping-times and suprema of the housekeeping heat. We test our results with numerical simulations of a system driven out of equilibrium and described by Langevin dynamics. △ Less

Submitted 13 January, 2019; v1 submitted 22 October, 2018; originally announced October 2018.

Comments: 7 pages, 2 figures

Journal ref: EPL 124,60006 (2018)

Testing Optimality of Sequential Decision-Making

Authors: Meik Dörpinghaus, Izaak Neri, Édgar Roldán, Heinrich Meyr, Frank Jülicher

Abstract: This paper provides a statistical method to test whether a system that performs a binary sequential hypothesis test is optimal in the sense of minimizing the average decision times while taking decisions with given reliabilities. The proposed method requires samples of the decision times, the decision outcomes, and the true hypotheses, but does not require knowledge on the statistics of the observ… ▽ More This paper provides a statistical method to test whether a system that performs a binary sequential hypothesis test is optimal in the sense of minimizing the average decision times while taking decisions with given reliabilities. The proposed method requires samples of the decision times, the decision outcomes, and the true hypotheses, but does not require knowledge on the statistics of the observations or the properties of the decision-making system. The method is based on fluctuation relations for decision time distributions which are proved for sequential probability ratio tests. These relations follow from the martingale property of probability ratios and hold under fairly general conditions. We illustrate these tests with numerical experiments and discuss potential applications. △ Less

Submitted 4 January, 2018; originally announced January 2018.

Comments: 42 pages, 7 figures

Extreme reductions of entropy in an electronic double dot

Authors: Shilpi Singh, Édgar Roldán, Izaak Neri, Ivan M. Khaymovich, Dmitry S. Golubev, Ville F. Maisi, Joonas T. Peltonen, Frank Jülicher, Jukka P. Pekola

Abstract: We experimentally study negative fluctuations of stochastic entropy production in an electronic double dot operating in nonequilibrium steady-state conditions. We record millions of random electron tunneling events at different bias points, thus collecting extensive statistics. We show that for all bias voltages the experimental average values of the minima of stochastic entropy production lie abo… ▽ More We experimentally study negative fluctuations of stochastic entropy production in an electronic double dot operating in nonequilibrium steady-state conditions. We record millions of random electron tunneling events at different bias points, thus collecting extensive statistics. We show that for all bias voltages the experimental average values of the minima of stochastic entropy production lie above $-k_B$, where $k_B$ is the Boltzmann constant, in agreement with recent theoretical predictions for nonequilibrium steady states. Furthermore, we also demonstrate that the experimental cumulative distribution of the entropy production minima is bounded, at all times and for all bias voltages, by a universal expression predicted by the theory. We also extend our theory by deriving a general bound for the average value of the maximum heat absorbed by a mesoscopic system from the environment and compare this result with experimental data. Finally, we show by numerical simulations that these results are not necessarily valid under non-stationary conditions. △ Less

Submitted 17 January, 2019; v1 submitted 5 December, 2017; originally announced December 2017.

Comments: 16 pages, 12 figures

Journal ref: Phys. Rev. B 99, 115422 (2019)

Generic Properties of Stochastic Entropy Production

Authors: Simone Pigolotti, Izaak Neri, Édgar Roldán, Frank Jülicher

Abstract: We derive an Ito stochastic differential equation for entropy production in nonequilibrium Langevin processes. Introducing a random-time transformation, entropy production obeys a one-dimensional drift-diffusion equation, independent of the underlying physical model. This transformation allows us to identify generic properties of entropy production. It also leads to an exact uncertainty equality r… ▽ More We derive an Ito stochastic differential equation for entropy production in nonequilibrium Langevin processes. Introducing a random-time transformation, entropy production obeys a one-dimensional drift-diffusion equation, independent of the underlying physical model. This transformation allows us to identify generic properties of entropy production. It also leads to an exact uncertainty equality relating the Fano factor of entropy production and the Fano factor of the random time, which we also generalize to non steady-state conditions. △ Less

Submitted 11 August, 2017; v1 submitted 13 April, 2017; originally announced April 2017.

Comments: 5 pages, 5 figures (contains Supplemental Material, 7 pages)

Journal ref: Phys. Rev. Lett. 119, 140604 (2017)

Cost of remembering a bit of information

Authors: Davide Chiuchiù, Miquel López-Suárez, Igor Neri, Maria Cristina Diamantini, Luca Gammaitoni

Abstract: In 1961, Rolf Landauer pointed out that resetting a binary memory requires a minimum energy of $k_BT \ln(2)$. However, once written, any memory is doomed to loose its content if no action is taken. To avoid memory losses, a refresh procedure is periodically performed. In this paper we present a theoretical model and an experiment on a micro-electro-mechanical system to evaluate the minimum energy… ▽ More In 1961, Rolf Landauer pointed out that resetting a binary memory requires a minimum energy of $k_BT \ln(2)$. However, once written, any memory is doomed to loose its content if no action is taken. To avoid memory losses, a refresh procedure is periodically performed. In this paper we present a theoretical model and an experiment on a micro-electro-mechanical system to evaluate the minimum energy required to preserve one bit of information over time. Two main conclusions are drawn: i) in principle the energetic cost to preserve information for a fixed time duration with a given error probability can be arbitrarily reduced if the refresh procedure is performed often enough; ii) the Heisenberg uncertainty principle sets an upper bound on the memory lifetime. △ Less

Submitted 10 May, 2018; v1 submitted 16 March, 2017; originally announced March 2017.

Comments: 15 pages, 5 figures

Journal ref: Phys. Rev. A 97, 052108 (2018)

Eigenvalue Outliers of non-Hermitian Random Matrices with a Local Tree Structure

Authors: Izaak Neri, Fernando Lucas Metz

Abstract: Spectra of sparse non-Hermitian random matrices determine the dynamics of complex processes on graphs. Eigenvalue outliers in the spectrum are of particular interest, since they determine the stationary state and the stability of dynamical processes. We present a general and exact theory for the eigenvalue outliers of random matrices with a local tree structure. For adjacency and Laplacian matrice… ▽ More Spectra of sparse non-Hermitian random matrices determine the dynamics of complex processes on graphs. Eigenvalue outliers in the spectrum are of particular interest, since they determine the stationary state and the stability of dynamical processes. We present a general and exact theory for the eigenvalue outliers of random matrices with a local tree structure. For adjacency and Laplacian matrices of oriented random graphs, we derive analytical expressions for the eigenvalue outliers, the first moments of the distribution of eigenvector elements associated with an outlier, the support of the spectral density, and the spectral gap. We show that these spectral observables obey universal expressions, which hold for a broad class of oriented random matrices. △ Less

Submitted 23 November, 2016; originally announced November 2016.

Comments: 25 pages, 4 figures

Journal ref: Phys. Rev. Lett. 117, 224101 (2016)

Electronic transport modulation on few-layers suspended MoS$_2$ under strain

Authors: Igor Neri, Miquel López-Suárez

Abstract: The production of new sensors, transducers and electronic components can benefit from the possibility to alter the electronic transport of metal-semicondutor-metal (MSM) devices. 2D materials are extremely appealing for those new technologies. This can determined by several phenomena as piezoelectric effect, piezoresistive effect and modulation of Schottky barrier. In particular, MoS$_2$, among ot… ▽ More The production of new sensors, transducers and electronic components can benefit from the possibility to alter the electronic transport of metal-semicondutor-metal (MSM) devices. 2D materials are extremely appealing for those new technologies. This can determined by several phenomena as piezoelectric effect, piezoresistive effect and modulation of Schottky barrier. In particular, MoS$_2$, among other Transition Metal Dichalcogenides (TMDs), is predicted to show a transition from semiconductor to metal under strain. In this article we present measurements on the modulation of electronic transport on few layer MoS$_2$ suspended ribbons under uniaxial tensile strain. Experimentally observed changes in the two terminal IV curves can be explained in terms of band gap closing in the semiconductor. A maximum gauge factor of 240 is achieved for a 3-layer ribbon. We also report on the fabrication process that allows to apply high strains to suspended MoS$_2$ ribbons, paving the way to future studies on the effect of strain in 2D materials. △ Less

Submitted 11 June, 2018; v1 submitted 30 September, 2016; originally announced September 2016.

Journal ref: Phys. Rev. B 97, 241408 (2018)

Heat production and error probability relation in Landauer reset at effective temperature

Authors: Igor Neri, Miquel López-Suárez

Abstract: The erasure of a classical bit of information is a dissipative process. The minimum heat produced during this operation has been theorized by Rolf Landauer in 1961 to be equal to $k_B T \ln 2$ and takes the name of Landauer limit, Landauer reset or Landauer principle. Despite its fundamental importance, the Landauer limit remained untested experimentally for more than fifty years until recently wh… ▽ More The erasure of a classical bit of information is a dissipative process. The minimum heat produced during this operation has been theorized by Rolf Landauer in 1961 to be equal to $k_B T \ln 2$ and takes the name of Landauer limit, Landauer reset or Landauer principle. Despite its fundamental importance, the Landauer limit remained untested experimentally for more than fifty years until recently when it has been tested using colloidal particles and magnetic dots. Experimental measurements on different devices, like micro-mechanical systems or nano-electronic devices are still missing. Here we show the results obtained in performing the Landauer reset operation in a micro-mechanical system, operated at an effective temperature. The measured heat exchange is in accordance with the theory reaching values close to the expected limit. The data obtained for the heat production is then correlated to the probability of error in accomplishing the reset operation. △ Less

Submitted 7 September, 2016; v1 submitted 16 July, 2016; originally announced July 2016.

Journal ref: Scientific Reports 6, Article number: 34039 (2016)

Micro-electromechanical memory bit based on magnetic repulsion

Authors: Miquel López-Suárez, Igor Neri

Abstract: A bistable micro-mechanical system based on magnetic repulsion is presented exploring its applicability as memory unit where the state of the bit is encoded in the rest position of a deflected cantilever. The non-linearity induced on the cantilever can be tuned through the magnetic interaction intensity between the cantilever magnet and the counter magnet in terms of geometrical parameters. A simp… ▽ More A bistable micro-mechanical system based on magnetic repulsion is presented exploring its applicability as memory unit where the state of the bit is encoded in the rest position of a deflected cantilever. The non-linearity induced on the cantilever can be tuned through the magnetic interaction intensity between the cantilever magnet and the counter magnet in terms of geometrical parameters. A simple model provides a sound prediction of the behavior of the system. Finally we measured the energy required to store a bit of information on the system that, for the considered protocols, is bounded by the energy barrier separating the two stable states. △ Less

Submitted 14 July, 2016; v1 submitted 2 May, 2016; originally announced May 2016.

Journal ref: Applied Physics Letters 2016 109:13

Band gap engineering of MoS$_2$ upon compression

Authors: Miquel López-Suárez, Igor Neri, Riccardo Rurali

Abstract: Molybdenum disulfide (MoS$_2$) is a promising candidate for 2D nanoelectronic devices, that shows a direct band-gap for monolayer structure. In this work we study the electronic structure of MoS$_2$ upon both compressive and tensile strains with first-principles density-functional calculations for different number of layers. The results show that the band-gap can be engineered for experimentally a… ▽ More Molybdenum disulfide (MoS$_2$) is a promising candidate for 2D nanoelectronic devices, that shows a direct band-gap for monolayer structure. In this work we study the electronic structure of MoS$_2$ upon both compressive and tensile strains with first-principles density-functional calculations for different number of layers. The results show that the band-gap can be engineered for experimentally attainable strains (i.e. $\pm 0.15$). However compressive strain can result in bucking that can prevent the use of large compressive strain. We then studied the stability of the compression, calculating the critical strain that results in the on-set of buckling for free-standing nanoribbons of different lengths. The results demonstrate that short structures, or few-layer MoS$_2$, show semi-conductor to metal transition upon compressive strain without bucking. △ Less

Submitted 30 April, 2016; originally announced May 2016.

Journal ref: Journal of Applied Physics, 119, 165105 (2016)

Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes

Authors: Izaak Neri, Édgar Roldán, Frank Jülicher

Abstract: We study the statistics of infima, stopping times and passage probabilities of entropy production in nonequilibrium steady states, and show that they are universal. We consider two examples of stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches for the first time a given state. Our main results are: (i) the… ▽ More We study the statistics of infima, stopping times and passage probabilities of entropy production in nonequilibrium steady states, and show that they are universal. We consider two examples of stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches for the first time a given state. Our main results are: (i) the distribution of the global infimum of entropy production is exponential with mean equal to minus Boltzmann's constant; (ii) we find the exact expressions for the passage probabilities of entropy production to reach a given value; (iii) we derive a fluctuation theorem for stopping-time distributions of entropy production. These results have interesting implications for stochastic processes that can be discussed in simple colloidal systems and in active molecular processes. In particular, we show that the timing and statistics of discrete chemical transitions of molecular processes, such as, the steps of molecular motors, are governed by the statistics of entropy production. We also show that the extreme-value statistics of active molecular processes are governed by entropy production, for example, the infimum of entropy production of a motor can be related to the maximal excursion of a motor against the direction of an external force. Using this relation, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases, which follows from our universal results for entropy-production infima. △ Less

Submitted 4 October, 2016; v1 submitted 14 April, 2016; originally announced April 2016.

Comments: 30 pages, 13 figures

Journal ref: Phys. Rev. X 7, 011019 (2017)

Sub $k_B T$ micro-electromechanical irreversible logic gate

Authors: Miquel Lopez-Suarez, Igor Neri, Luca Gammaitoni

Abstract: In modern computers, computation is performed by assembling together sets of logic gates. Popular gates like AND, OR, XOR, processing two logic inputs and yielding one logic output, are often addressed as irreversible logic gates where the sole knowledge of the output logic value, is not sufficient to infer the logic value of the two inputs. Such gates are usually believed to be bounded to dissipa… ▽ More In modern computers, computation is performed by assembling together sets of logic gates. Popular gates like AND, OR, XOR, processing two logic inputs and yielding one logic output, are often addressed as irreversible logic gates where the sole knowledge of the output logic value, is not sufficient to infer the logic value of the two inputs. Such gates are usually believed to be bounded to dissipate a finite minimum amount of energy determined by the input-output information difference. Here we show that this is not necessarily the case, by presenting an experiment where a OR logic gate, realized with a micro electromechanical cantilever, is operated with energy well below the expected limit, provided the operation is slow enough and frictional phenomena are properly addressed. △ Less

Submitted 28 June, 2016; v1 submitted 11 August, 2015; originally announced August 2015.

Journal ref: Nature Communications 7, 12068 (2016)

Decision Making in the Arrow of Time

Authors: Édgar Roldán, Izaak Neri, Meik Dörpinghaus, Heinrich Meyr, Frank Jülicher

Abstract: We show that the steady-state entropy production rate of a stochastic process is inversely proportional to the minimal time needed to decide on the direction of the arrow of time. Here we apply Wald's sequential probability ratio test to optimally decide on the direction of time's arrow in stationary Markov processes. Furthermore the steady state entropy production rate can be estimated using mean… ▽ More We show that the steady-state entropy production rate of a stochastic process is inversely proportional to the minimal time needed to decide on the direction of the arrow of time. Here we apply Wald's sequential probability ratio test to optimally decide on the direction of time's arrow in stationary Markov processes. Furthermore the steady state entropy production rate can be estimated using mean first-passage times of suitable physical variables. We derive a first-passage time fluctuation theorem which implies that the decision time distributions for correct and wrong decisions are equal. Our results are illustrated by numerical simulations of two simple examples of nonequilibrium processes. △ Less

Submitted 17 December, 2015; v1 submitted 9 August, 2015; originally announced August 2015.

Comments: 9 pages, 5 figures

Journal ref: Phys. Rev. Lett. 115, 250602 (2015)

Reset and switch protocols at Landauer limit in a graphene buckled ribbon

Authors: I. Neri, M. Lopez-Suarez, D. Chiuchiu', L. Gammaitoni

Abstract: Heat produced during a reset operation is meant to show a fundamental bound known as Landauer limit, while simple switch operations have an expected minimum amount of produced heat equal to zero. However, in both cases, present-day technology realizations dissipate far beyond these theoretical limits. In this paper we present a study based on molecular dynamics simulations, where reset and switch… ▽ More Heat produced during a reset operation is meant to show a fundamental bound known as Landauer limit, while simple switch operations have an expected minimum amount of produced heat equal to zero. However, in both cases, present-day technology realizations dissipate far beyond these theoretical limits. In this paper we present a study based on molecular dynamics simulations, where reset and switch protocols are applied on a graphene buckled ribbon, employed here as a nano electromechanical switch working at the thermodynamic limit. △ Less

Submitted 27 July, 2015; originally announced July 2015.

Journal ref: EPL, 111 (2015) 10004

Motor proteins traffic regulation by supply-demand balance of resources

Authors: Luca Ciandrini, I. Neri, Jean-Charles Walter, O. Dauloudet, A. Parmeggiani

Abstract: In cells and in vitro assays the number of motor proteins involved in biological transport processes is far from being unlimited. The cytoskeletal binding sites are in contact with the same finite reservoir of motors (either the cytosol or the flow chamber) and hence compete for recruiting the available motors, potentially depleting the reservoir and affecting cytoskeletal transport. In this work… ▽ More In cells and in vitro assays the number of motor proteins involved in biological transport processes is far from being unlimited. The cytoskeletal binding sites are in contact with the same finite reservoir of motors (either the cytosol or the flow chamber) and hence compete for recruiting the available motors, potentially depleting the reservoir and affecting cytoskeletal transport. In this work we provide a theoretical framework to study, analytically and numerically, how motor density profiles and crowding along cytoskeletal filaments depend on the competition of motors for their binding sites. We propose two models in which finite processive motor proteins actively advance along cytoskeletal filaments and are continuously exchanged with the motor pool. We first look at homogeneous reservoirs and then examine the effects of free motor diffusion in the surrounding medium. We consider as a reference situation recent in vitro experimental setups of kinesin-8 motors binding and moving along microtubule filaments in a flow chamber. We investigate how the crowding of linear motor proteins moving on a filament can be regulated by the balance between supply (concentration of motor proteins in the flow chamber) and demand (total number of polymerised tubulin heterodimers). We present analytical results for the density profiles of bound motors, the reservoir depletion, and propose novel phase diagrams that present the formation of jams of motor proteins on the filament as a function of two tuneable experimental parameters: the motor protein concentration and the concentration of tubulins polymerized into cytoskeletal filaments. Extensive numerical simulations corroborate the analytical results for parameters in the experimental range and also address the effects of diffusion of motor proteins in the reservoir. △ Less

Submitted 24 September, 2014; v1 submitted 13 August, 2014; originally announced August 2014.

Comments: 31 pages, 10 figures

Journal ref: Phys. Biol. 11 (2014) 056006

Exclusion processes on networks as models for cytoskeletal transport

Authors: I. Neri, N. Kern, A. Parmeggiani

Abstract: We present a study of exclusion processes on networks as models for complex transport phenomena and in particular for active transport of motor proteins along the cytoskeleton. We argue that active transport processes on networks spontaneously develop density heterogeneities at various scales. These heterogeneities can be regulated through a variety of multi-scale factors, such as the interplay of… ▽ More We present a study of exclusion processes on networks as models for complex transport phenomena and in particular for active transport of motor proteins along the cytoskeleton. We argue that active transport processes on networks spontaneously develop density heterogeneities at various scales. These heterogeneities can be regulated through a variety of multi-scale factors, such as the interplay of exclusion interactions, the non-equilibrium nature of the transport process and the network topology. We show how an effective rate approach allows to develop an understanding of the stationary state of transport processes through complex networks from the phase diagram of one single segment. For exclusion processes we rationalize that the stationary state can be classified in three qualitatively different regimes: a homogeneous phase as well as inhomogeneous network and segment phases. In particular, we present here a study of the stationary state on networks of three paradigmatic models from non-equilibrium statistical physics: the totally asymmetric simple exclusion process, the partially asymmetric simple exclusion process and the totally asymmetric simple exclusion process with Langmuir kinetics. With these models we can interpolate between equilibrium (due to bi-directional motion along a network or infinite diffusion) and out-of-equilibrium active directed motion along a network. The study of these models sheds further light on the emergence of density heterogeneities in active phenomena. △ Less

Submitted 6 April, 2013; originally announced April 2013.

Comments: 55 pages, 26 figures

Journal ref: New J. Phys. 15 (2013) 085005

Modelling cytoskeletal traffic: an interplay between passive diffusion and active transport

Authors: I. Neri, N. Kern, A. Parmeggiani

Abstract: We introduce the totally asymmetric exclusion process with Langmuir kinetics (TASEP-LK) on a network as a microscopic model for active motor protein transport on the cytoskeleton, immersed in the diffusive cytoplasm. We discuss how the interplay between active transport along a network and infinite diffusion in a bulk reservoir leads to a heterogeneous matter distribution on various scales. We fin… ▽ More We introduce the totally asymmetric exclusion process with Langmuir kinetics (TASEP-LK) on a network as a microscopic model for active motor protein transport on the cytoskeleton, immersed in the diffusive cytoplasm. We discuss how the interplay between active transport along a network and infinite diffusion in a bulk reservoir leads to a heterogeneous matter distribution on various scales. We find three regimes for steady state transport, corresponding to the scale of the network, of individual segments or local to sites. At low exchange rates strong density heterogeneities develop between different segments in the network. In this regime one has to consider the topological complexity of the whole network to describe transport. In contrast, at moderate exchange rates the transport through the network decouples, and the physics is determined by single segments and the local topology. At last, for very high exchange rates the homogeneous Langmuir process dominates the stationary state. We introduce effective rate diagrams for the network to identify these different regimes. Based on this method we develop an intuitive but generic picture of how the stationary state of excluded volume processes on complex networks can be understood in terms of the single-segment phase diagram. △ Less

Submitted 3 December, 2012; originally announced December 2012.

Comments: 5 pages, 7 figures

Journal ref: Phys. Rev. Lett. 110, 098102 (2013)

On the spectra of large sparse graphs with cycles

Authors: D. Bollé, F. L. Metz, I. Neri

Abstract: We present a general method for obtaining the spectra of large graphs with short cycles using ideas from statistical mechanics of disordered systems. This approach leads to an algorithm that determines the spectra of graphs up to a high accuracy. In particular, for (un)directed regular graphs with cycles of arbitrary length we derive exact and simple equations for the resolvent of the associated a… ▽ More We present a general method for obtaining the spectra of large graphs with short cycles using ideas from statistical mechanics of disordered systems. This approach leads to an algorithm that determines the spectra of graphs up to a high accuracy. In particular, for (un)directed regular graphs with cycles of arbitrary length we derive exact and simple equations for the resolvent of the associated adjacency matrix. Solving these equations we obtain analytical formulas for the spectra and the boundaries of their support. △ Less

Submitted 11 January, 2023; v1 submitted 7 June, 2012; originally announced June 2012.

Comments: 23 pages, 8 figures, a few typos have been corrected in the latest version

Journal ref: Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy's 60th Birthday, H. Holden et al. (eds), Proceedings of Symposia in Pure Mathematics, vol. 87, Amer. Math. Soc., pp. 35-58 (2013)

Spectra of sparse non-Hermitian random matrices: an analytical solution

Authors: I. Neri, F. L. Metz

Abstract: We present the exact analytical expression for the spectrum of a sparse non-Hermitian random matrix ensemble, generalizing two classical results in random-matrix theory: this analytical expression forms a non-Hermitian version of the Kesten-Mckay law as well as a sparse realization of Girko's elliptic law. Our exact result opens new perspectives in the study of several physical problems modelled o… ▽ More We present the exact analytical expression for the spectrum of a sparse non-Hermitian random matrix ensemble, generalizing two classical results in random-matrix theory: this analytical expression forms a non-Hermitian version of the Kesten-Mckay law as well as a sparse realization of Girko's elliptic law. Our exact result opens new perspectives in the study of several physical problems modelled on sparse random graphs. In this context, we show analytically that the convergence rate of a transport process on a very sparse graph depends upon the degree of symmetry of the edges in a non-monotonous way. △ Less

Submitted 23 December, 2012; v1 submitted 3 May, 2012; originally announced May 2012.

Comments: 5 pages, 5 figures, 12 pages supplemental material

Journal ref: Phys. Rev. Lett. 109, 030602 (2012)

Spectra of sparse regular graphs with loops

Authors: F. L. Metz, I. Neri, D. Bollé

Abstract: We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks are discussed by showing how loops influence the size of the spectral gap and the propensity for synchronization. Analytical formulas for the spectrum are obtain… ▽ More We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks are discussed by showing how loops influence the size of the spectral gap and the propensity for synchronization. Analytical formulas for the spectrum are obtained for specific length of the loops. △ Less

Submitted 20 July, 2011; originally announced July 2011.

Comments: 4 pages, 4 figures

Journal ref: Phys. Rev. E 84, 055101(R) (2011)

The totally asymmetric simple exclusion process on networks

Authors: I. Neri, N. Kern, A. Parmeggiani

Abstract: We study the totally asymmetric simple exclusion process (TASEP) on complex networks, as a paradigmatic model for transport subject to excluded volume interactions. Building on TASEP phenomenology on a single segment and borrowing ideas from random networks we investigate the effect of connectivity on transport. In particular, we argue that the presence of disorder in the topology of vertices cruc… ▽ More We study the totally asymmetric simple exclusion process (TASEP) on complex networks, as a paradigmatic model for transport subject to excluded volume interactions. Building on TASEP phenomenology on a single segment and borrowing ideas from random networks we investigate the effect of connectivity on transport. In particular, we argue that the presence of disorder in the topology of vertices crucially modifies the transport features of a network: irregular networks involve homogeneous segments and have a bimodal distribution of edge densities, whereas regular networks are dominated by shocks leading to a unimodal density distribution. The proposed numerical approach of solving for mean-field transport on networks provides a general framework for studying TASEP on large networks, and is expected to generalize to other transport processes. △ Less

Submitted 23 June, 2011; v1 submitted 14 May, 2011; originally announced May 2011.

Comments: 4 pages, 4 figures, accepted for publication in PRL

Journal ref: Phys. Rev. Lett. 107, 068702 (2011)

On the localization transition in symmetric random matrices

Authors: F. L. Metz, I. Neri, D. Bollé

Abstract: We study the behaviour of the inverse participation ratio and the localization transition in infinitely large random matrices through the cavity method. Results are shown for two ensembles of random matrices: Laplacian matrices on sparse random graphs and fully-connected Lévy matrices. We derive a critical line separating localized from extended states in the case of Lévy matrices. Comparison betw… ▽ More We study the behaviour of the inverse participation ratio and the localization transition in infinitely large random matrices through the cavity method. Results are shown for two ensembles of random matrices: Laplacian matrices on sparse random graphs and fully-connected Lévy matrices. We derive a critical line separating localized from extended states in the case of Lévy matrices. Comparison between theoretical results and diagonalization of finite random matrices is shown. △ Less

Submitted 30 September, 2010; v1 submitted 20 May, 2010; originally announced May 2010.

Comments: 10 pages, 6 figures

Journal ref: Phys. Rev. E 82, 031135 (2010)

The phase diagram of Lévy spin glasses

Authors: I. Neri, F. L. Metz, D. Bollé

Abstract: We study the Lévy spin-glass model with the replica and the cavity method. In this model each spin interacts through a finite number of strong bonds and an infinite number of weak bonds. This hybrid behaviour of Lévy spin glasses becomes transparent in our solution: the local field contains a part propagating along a backbone of strong bonds and a Gaussian noise term due to weak bonds. Our metho… ▽ More We study the Lévy spin-glass model with the replica and the cavity method. In this model each spin interacts through a finite number of strong bonds and an infinite number of weak bonds. This hybrid behaviour of Lévy spin glasses becomes transparent in our solution: the local field contains a part propagating along a backbone of strong bonds and a Gaussian noise term due to weak bonds. Our method allows to determine the complete replica symmetric phase diagram, the replica symmetry breaking line and the entropy. The results are compared with simulations and previous calculations using a Gaussian ansatz for the distribution of fields. △ Less

Submitted 7 October, 2009; originally announced October 2009.

Comments: 20 pages, 7 figures

Journal ref: J. Stat. Mech. (2010) P01010

Statistical mechanics of LDPC codes on channels with memory

Authors: I. Neri, N. S. Skantzos

Abstract: We present an analytic method of assessing the typical performance of low-density parity-check codes on finite-state Markov channels. We show that this problem is similar to a spin-glass model on a `small-world' lattice. We apply our methodology to binary-symmetric and binary-asymmetric channels and we provide the critical noise levels for different degrees of channel symmetry. We present an analytic method of assessing the typical performance of low-density parity-check codes on finite-state Markov channels. We show that this problem is similar to a spin-glass model on a `small-world' lattice. We apply our methodology to binary-symmetric and binary-asymmetric channels and we provide the critical noise levels for different degrees of channel symmetry. △ Less

Submitted 4 July, 2009; originally announced July 2009.

Comments: 6 pages, 4 figures

Journal ref: J. Phys. A: Math. Theor. 47 (2014) 385002

The Cavity Approach to Parallel Dynamics of Ising Spins on a Graph

Authors: I. Neri, D. Bollé

Abstract: We use the cavity method to study parallel dynamics of disordered Ising models on a graph. In particular, we derive a set of recursive equations in single site probabilities of paths propagating along the edges of the graph. These equations are analogous to the cavity equations for equilibrium models and are exact on a tree. On graphs with exclusively directed edges we find an exact expression for… ▽ More We use the cavity method to study parallel dynamics of disordered Ising models on a graph. In particular, we derive a set of recursive equations in single site probabilities of paths propagating along the edges of the graph. These equations are analogous to the cavity equations for equilibrium models and are exact on a tree. On graphs with exclusively directed edges we find an exact expression for the stationary distribution of the spins. We present the phase diagrams for an Ising model on an asymmetric Bethe lattice and for a neural network with Hebbian interactions on an asymmetric scale-free graph. For graphs with a nonzero fraction of symmetric edges the equations can be solved for a finite number of time steps. Theoretical predictions are confirmed by simulation results. Using a heuristic method, the cavity equations are extended to a set of equations that determine the marginals of the stationary distribution of Ising models on graphs with a nonzero fraction of symmetric edges. The results of this method are discussed and compared with simulations. △ Less

Submitted 22 April, 2025; v1 submitted 20 May, 2009; originally announced May 2009.

Journal ref: J. Stat. Mech. (2009) P08009

Universal and reconfigurable logic gates in a noise-triggered artificial neuron node

Authors: L. Worschech, F. Hartmann, A. Forchel, J. Ahopelto, I. Neri, L. Gammaitoni

Abstract: Submicron-sized mesas of resonant tunneling diodes (RTDs) with split drain contacts have been realized and the current-voltage characteristics have been studied in the bistable regime at room temperature. Dynamically-biased, the RTDs show noise-triggered firing of spike-like signals and can act as reconfigurable universal logic gates for small voltage changes of a few mV at the input branches. T… ▽ More Submicron-sized mesas of resonant tunneling diodes (RTDs) with split drain contacts have been realized and the current-voltage characteristics have been studied in the bistable regime at room temperature. Dynamically-biased, the RTDs show noise-triggered firing of spike-like signals and can act as reconfigurable universal logic gates for small voltage changes of a few mV at the input branches. These observations are interpreted in terms of a stochastic nonlinear processes in the split RTD, which are found to be robust against noise. The split RTDs show also gain for the fired-signal bursts, can be easily integrated to arrays of multiple inputs and have thus the potential to mimic neuron nodes in nanoelectronic circuits. △ Less

Submitted 19 December, 2008; originally announced December 2008.

Comments: 4 pages, 6 figures