Showing 1–48 of 48 results for author: Fodor, E

Topology of pulsating active matter: Defect asymmetry controls emergent motility

Authors: Luca Casagrande, Alessandro Manacorda, Étienne Fodor

Abstract: In pulsating active matter, topological defects are motile despite the absence of any macroscopic flows and microscopic self-propulsion. We reveal that this motility arises from a ratchet effect: the mechanochemical coupling between local oscillations and repulsive interactions breaks both spatial and time-reversal symmetries, thus leading asymmetric rotating defects to drift under fluctuations. T… ▽ More In pulsating active matter, topological defects are motile despite the absence of any macroscopic flows and microscopic self-propulsion. We reveal that this motility arises from a ratchet effect: the mechanochemical coupling between local oscillations and repulsive interactions breaks both spatial and time-reversal symmetries, thus leading asymmetric rotating defects to drift under fluctuations. This mechanism regulates a crossover between spiral waves connecting slow defects and fiber-like waves connecting fast defects, in analogy with the onset of heart rhythm disorder in cardiac tissues. We rationalize this crossover in terms of a fluctuating hydrodynamics that captures how motile defects spontaneously nucleate and move within an ordered background. △ Less

Submitted 8 July, 2026; v1 submitted 25 May, 2026; originally announced May 2026.

Collective deformation of anisotropic particles with internal pulsation

Authors: Luca Casagrande, Alessandro Manacorda, Étienne Fodor

Abstract: Capturing the emergence of deformation waves in contractile living tissues is a challenge that has recently been tackled with models of actively deformable particles. Inspired by the anisotropic deformation of cardiomyocytes in cardiac tissues, we examine how the pulsation of elliptical particles affects their collective properties in dense assemblies. We introduce two types of deformation where t… ▽ More Capturing the emergence of deformation waves in contractile living tissues is a challenge that has recently been tackled with models of actively deformable particles. Inspired by the anisotropic deformation of cardiomyocytes in cardiac tissues, we examine how the pulsation of elliptical particles affects their collective properties in dense assemblies. We introduce two types of deformation where the eccentricity of each particle is subject to a periodic drive, and examine the interplay between nematic order and synchronized deformation via a systematic phase diagram. We derive a hydrodynamic description through a coarse-graining procedure, and show that it qualitatively captures the main collective states of the microscopic dynamics. Overall, our model provides key insights into how an active anisotropic deformation yields waves that self-organize into various dynamical patterns. △ Less

Submitted 11 August, 2026; v1 submitted 25 May, 2026; originally announced May 2026.

Contraction waves in pulsating active liquids: From pacemaker to aster dynamics

Authors: Tirthankar Banerjee, Thibault Desaleux, Jonas Ranft, Étienne Fodor

Abstract: We propose a hydrodynamic theory to examine the emergence of contraction waves in dense active liquids composed of pulsating deformable particles. Our theory couples the liquid density with a chemical phase that determines the periodic deformation of the particles. This mechanochemical coupling regulates the interplay between the flow induced by local deformation, and the resistance to pulsation s… ▽ More We propose a hydrodynamic theory to examine the emergence of contraction waves in dense active liquids composed of pulsating deformable particles. Our theory couples the liquid density with a chemical phase that determines the periodic deformation of the particles. This mechanochemical coupling regulates the interplay between the flow induced by local deformation, and the resistance to pulsation stemming from steric interaction. We show that this interplay leads the emergent contraction waves to spontaneously organize into a packing of pacemakers. We reveal that the dynamics of these pacemakers is governed by a complex feedback between slow and fast topological defects that form asters in velocity flows. In fact, our defect analysis is a versatile platform for investigating the self-organization of waves in a wide range of contractile systems. Our results shed light on the key mechanisms that control the rich phenomenology of pulsating liquids, with relevance for biological systems such as tissues made of confluent pulsating cells. △ Less

Submitted 23 September, 2025; originally announced September 2025.

Comments: 8 pages, 4 figures

Irreversibility in scalar active turbulence: The role of topological defects

Authors: Byjesh N. Radhakrishnan, Francesco Serafin, Thomas L. Schmidt, Étienne Fodor

Abstract: In many active systems, swimmers collectively stir the surrounding fluid to stabilize some self-sustained vortices. The resulting nonequilibrium state is often referred to as active turbulence, by analogy with the turbulence of passive fluids under external stirring. Although active turbulence clearly operates far from equilibrium, it can be challenging to pinpoint which emergent features primaril… ▽ More In many active systems, swimmers collectively stir the surrounding fluid to stabilize some self-sustained vortices. The resulting nonequilibrium state is often referred to as active turbulence, by analogy with the turbulence of passive fluids under external stirring. Although active turbulence clearly operates far from equilibrium, it can be challenging to pinpoint which emergent features primarily control the deviation from an equilibrium reversible dynamics. Here, we reveal that dynamical irreversibility essentially stems from singularities in the active stress. Specifically, considering the coupled dynamics of the swimmer density and the stream function, we demonstrate that the symmetries of vortical flows around defects determine the overall irreversibility. Our detailed analysis leads to identifying specific configurations of defect pairs as the dominant contribution to irreversibility. △ Less

Submitted 2 March, 2026; v1 submitted 8 July, 2025; originally announced July 2025.

Comments: 30 pages, 10 figures. Supplementary movie in the published version

Journal ref: New J. Phys. 28 034601 (2026)

Entropy production rate in thermodynamically consistent flocks

Authors: Tal Agranov, Robert L. Jack, Michael E. Cates, Étienne Fodor

Abstract: We study the entropy production rate (EPR) of aligning self-propelled particles which undergo a flocking transition towards a polarized collective motion. In our thermodynamically consistent lattice model, individual self-propulsion is the exclusive source of irreversibility. We derive the fluctuating hydrodynamics for large system sizes using a controlled coarse-graining: our procedure entails an… ▽ More We study the entropy production rate (EPR) of aligning self-propelled particles which undergo a flocking transition towards a polarized collective motion. In our thermodynamically consistent lattice model, individual self-propulsion is the exclusive source of irreversibility. We derive the fluctuating hydrodynamics for large system sizes using a controlled coarse-graining: our procedure entails an exact correspondence between the EPR evaluated at the hydrodynamic and particle-based levels. We reveal that EPR is maximal when the system adopts a homogeneous configuration, either apolar or polar, and reduced in the non-homogeneous state where a polar band travels in a apolar background due to strong spatial EPR modulations. By analyzing the latter we also show that asymmetric energetic exchanges occur at the trailing and leading edges, which we map into a thermodynamic cycle in density-polarization space. Finally, we demonstrate that the regime of weak self-propulsion features a singular scaling of EPR, and a non-analyticity of the travelling band profiles. △ Less

Submitted 19 May, 2025; originally announced May 2025.

Comments: 33 pages, 9 figures

Journal ref: New J. Phys. 27, 104602 (2025)

Quantifying dissipation in flocking dynamics: When tracking internal states matters

Authors: Karel Proesmans, Gianmaria Falasco, Atul Tanaji Mohite, Massimiliano Esposito, Étienne Fodor

Abstract: Aligning self-propelled particles undergo a nonequilibrium flocking transition from apolar to polar phases as their interactions become stronger. We propose a thermodynamically consistent lattice model, in which the internal state of the particles biases their diffusion, to capture such a transition. Changes of internal states and jumps between lattice sites obey local detailed balance with respec… ▽ More Aligning self-propelled particles undergo a nonequilibrium flocking transition from apolar to polar phases as their interactions become stronger. We propose a thermodynamically consistent lattice model, in which the internal state of the particles biases their diffusion, to capture such a transition. Changes of internal states and jumps between lattice sites obey local detailed balance with respect to the same interaction energy. We unveil a crossover between two regimes: for weak interactions, the dissipation is maximal, and partial inference (namely, based on discarding the dynamics of internal states) leads to a severe underestimation; for strong interactions, the dissipation is reduced, and partial inference captures most of the dissipation. Finally, we reveal that the macroscopic dissipation, evaluated at the hydrodynamic level, coincides with the microscopic dissipation upon coarse-graining. We argue that this correspondence stems from a generic mapping of active lattice models with local detailed balance into a specific class of non-ideal reaction-diffusion systems. △ Less

Submitted 28 May, 2025; v1 submitted 19 May, 2025; originally announced May 2025.

Comments: 11 pages, 4 figures

Journal ref: Phys. Rev. E 112, 024103 (2025)

Control of active field theories at minimal dissipation

Authors: Artur Soriani, Elsen Tjhung, Étienne Fodor, Tomer Markovich

Abstract: Advances in experimental techniques enable the precise manipulation of a large variety of active systems, which constantly dissipate energy to sustain nonequilibrium phenomena without any equilibrium equivalent. To design novel materials out of active systems, an outstanding challenge is to rationalize how material properties can be optimally controlled by applying external perturbations. However,… ▽ More Advances in experimental techniques enable the precise manipulation of a large variety of active systems, which constantly dissipate energy to sustain nonequilibrium phenomena without any equilibrium equivalent. To design novel materials out of active systems, an outstanding challenge is to rationalize how material properties can be optimally controlled by applying external perturbations. However, equilibrium thermodynamics is inadequate to guide the control of such nonequilibrium systems. Therefore, there is a dire need for a novel framework to provide a systematic toolbox for the thermodynamic control of active matter. Here, we build an optimization procedure for generic active field theories within a thermodynamically consistent formulation. Central to our approach is the distinction between the protocol heat, which is dissipated only during manipulation, and the total heat, which also accounts for the post-manipulation dissipation. We demonstrate that the latter generically features a global minimum with respect to the protocol duration. We deploy our versatile approach to an active theory of phase separation, and examine the scalings of the optimal protocol duration with respect to activity and system size. Remarkably, we reveal that the landscape of steady-state dissipation regulates the crossover between optimal control strategies for a finite duration. △ Less

Submitted 2 June, 2025; v1 submitted 27 April, 2025; originally announced April 2025.

Comments: 12 pages, 5 figures

Species interconversion of deformable particles yields transient phase separation

Authors: Yiwei Zhang, Alessandro Manacorda, Étienne Fodor

Abstract: We consider a dense assembly of repulsive particles whose fluctuating sizes are subject to an energetic landscape that defines three species: two distinct states of particles with a finite size, and point particles as an intermediate state between the two previous species. We show that the non-equilibrium synchronization of sizes systematically leads to a homogeneous configuration associated with… ▽ More We consider a dense assembly of repulsive particles whose fluctuating sizes are subject to an energetic landscape that defines three species: two distinct states of particles with a finite size, and point particles as an intermediate state between the two previous species. We show that the non-equilibrium synchronization of sizes systematically leads to a homogeneous configuration associated with the survival of a single species. Remarkably, the relaxation towards such a configuration features a transient phase separation. By delineating and analyzing the dominant kinetic factors at play during relaxation, we recapitulate the phase diagram of species survival in terms of the parameters of the size landscape. Finally, we obtain a hydrodynamic mapping to equilibrium by coarse-graining the microscopic dynamics, which leads to predicting the nature of the transitions between various regimes where distinct species survive. △ Less

Submitted 28 April, 2025; v1 submitted 13 January, 2025; originally announced January 2025.

Comments: 18 pages, 7 figures

Journal ref: New J. Phys. 27 (2025) 043023

Hydrodynamics of pulsating active liquids

Authors: Tirthankar Banerjee, Thibault Desaleux, Jonas Ranft, Étienne Fodor

Abstract: Inspired by dense contractile tissues, where cells are subject to periodic deformation, we formulate and study a generic hydrodynamic theory of pulsating active liquids. Combining mechanical and phenomenological arguments, we postulate that the mechanochemical feedback between the local phase, which describes how cells deform due to autonomous driving, and the local density can be described in ter… ▽ More Inspired by dense contractile tissues, where cells are subject to periodic deformation, we formulate and study a generic hydrodynamic theory of pulsating active liquids. Combining mechanical and phenomenological arguments, we postulate that the mechanochemical feedback between the local phase, which describes how cells deform due to autonomous driving, and the local density can be described in terms of a free energy. We demonstrate that such a feedback is compatible with the coarse-graining of a broad class of microscopic models. Our hydrodynamics captures the three main states emerging in its particle-based counterparts: a globally cycling state, a homogeneous arrested state with constant phase, and a state with propagating radial waves. Remarkably, we show that the competition between these states can be rationalized intuitively in terms of an effective landscape, and argue that waves can be regarded as secondary instabilities. Linear stability analysis of the arrested and cycling states, including the role of fluctuations, leads to predictions for the phase boundaries. Overall, our results demonstrate that our minimal, yet non-trivial model provides a relevant platform to study the rich phenomenology of pulsating liquids. △ Less

Submitted 24 September, 2025; v1 submitted 29 July, 2024; originally announced July 2024.

Comments: 21 pages, 7 figures

Nonequilibrium Thermodynamics of Non-Ideal Reaction-Diffusion Systems: Implications for Active Self-Organization

Authors: Francesco Avanzini, Timur Aslyamov, Étienne Fodor, Massimiliano Esposito

Abstract: We develop a framework describing the dynamics and thermodynamics of open non-ideal reaction-diffusion systems, which embodies Flory-Huggins theories of mixtures and chemical reaction network theories. Our theory elucidates the mechanisms underpinning the emergence of self-organized dissipative structures in these systems. It evaluates the dissipation needed to sustain and control them, discrimina… ▽ More We develop a framework describing the dynamics and thermodynamics of open non-ideal reaction-diffusion systems, which embodies Flory-Huggins theories of mixtures and chemical reaction network theories. Our theory elucidates the mechanisms underpinning the emergence of self-organized dissipative structures in these systems. It evaluates the dissipation needed to sustain and control them, discriminating the contributions from each reaction and diffusion process with spatial resolution. It also reveals the role of the reaction network in powering and shaping these structures. We identify particular classes of networks in which diffusion processes always equilibrate within the structures, while dissipation occurs solely due to chemical reactions. The spatial configurations resulting from these processes can be derived by minimizing a kinetic potential, contrasting with the minimization of the thermodynamic free energy in passive systems. This framework opens the way to investigating the energetic cost of phenomena such as liquid-liquid phase separation, coacervation, and the formation of biomolecular condensates. △ Less

Submitted 15 October, 2024; v1 submitted 12 July, 2024; originally announced July 2024.

Journal ref: J. Chem. Phys. 161, 174108 (2024)

Biased ensembles of pulsating active matter

Authors: William D. Piñeros, Étienne Fodor

Abstract: We discover unexpected connections between packing configurations and rare fluctuations in dense systems of active particles subject to pulsation of size. Using large deviation theory, we examine biased ensembles which select atypical realizations of the dynamics exhibiting high synchronization in particle size. We show that the order emerging at high bias can manifest as distinct dynamical states… ▽ More We discover unexpected connections between packing configurations and rare fluctuations in dense systems of active particles subject to pulsation of size. Using large deviation theory, we examine biased ensembles which select atypical realizations of the dynamics exhibiting high synchronization in particle size. We show that the order emerging at high bias can manifest as distinct dynamical states featuring high to vanishing pulsation current. Remarkably, transitions between these states arise from changing the system geometry at fixed bias and constant density. We rationalize such transitions as arising from the change in packing configurations which, depending on box geometry, may induce highly ordered or geometrically frustrated structures. Furthermore, we reveal that a master curve in the unbiased dynamics, correlating polydispersity and current, helps predict the dynamical state emerging in the biased dynamics. Finally, we demonstrate that deformation waves can propagate under suitable geometries when biasing with local order. △ Less

Submitted 3 January, 2025; v1 submitted 25 March, 2024; originally announced March 2024.

Comments: 6 pages, 4 figures in main text, 1 appendix figure; supplemental; includes data and code availability information

Journal ref: Phys. Rev. Lett. 134, 038301 (2025)

Thermodynamically consistent flocking: From discontinuous to continuous transitions

Authors: Tal Agranov, Robert L. Jack, Michael E. Cates, Étienne Fodor

Abstract: We introduce a family of lattice-gas models of flocking, whose thermodynamically consistent dynamics admits a proper equilibrium limit at vanishing self-propulsion. These models are amenable to an exact coarse-graining which allows us to study their hydrodynamic behavior analytically. We show that the equilibrium limit here belongs to the universality class of Model C, and that it generically exhi… ▽ More We introduce a family of lattice-gas models of flocking, whose thermodynamically consistent dynamics admits a proper equilibrium limit at vanishing self-propulsion. These models are amenable to an exact coarse-graining which allows us to study their hydrodynamic behavior analytically. We show that the equilibrium limit here belongs to the universality class of Model C, and that it generically exhibits tricritical behavior. Self-propulsion has a non-perturbative effect on the phase diagram, yielding novel phase behaviors depending on the type of aligning interactions. For aligning interactions that increase monotonically with the density, the tricritical point diverges to infinite density reproducing the standard scenario of a discontinuous flocking transition accompanied by traveling bands. In contrast, for models where the aligning interaction is non-monotonic in density, the system can exhibit either (the nonequilibrium counterpart of) an azeotropic point, associated with a continuous flocking transition, or a state with counterpropagating bands. △ Less

Submitted 20 May, 2024; v1 submitted 18 January, 2024; originally announced January 2024.

Journal ref: New J. Phys. 26, 063006 (2024)

Diffusive oscillators capture the pulsating states of deformable particles

Authors: Alessandro Manacorda, Étienne Fodor

Abstract: We study a model of diffusive oscillators whose internal states are subject to a periodic drive. These models are inspired by the dynamics of deformable particles with pulsating sizes, where repulsion leads to arrest the internal pulsation at high density. We reveal that, despite the absence of any repulsion between the diffusive oscillators, our model still captures the emergence of dynamical arr… ▽ More We study a model of diffusive oscillators whose internal states are subject to a periodic drive. These models are inspired by the dynamics of deformable particles with pulsating sizes, where repulsion leads to arrest the internal pulsation at high density. We reveal that, despite the absence of any repulsion between the diffusive oscillators, our model still captures the emergence of dynamical arrest. We demonstrate that arrest here stems from the discrete nature of internal states which enforces an effective energy landscape analogous to that of deformable particles. Moreover, we show that the competition between arrest and synchronisation promotes spiral waves reminiscent of the pulsating states of deformable particles. Using analytical coarse-graining, we derive and compare the collective dynamics of diffusive oscillators with that of deformable particles. This comparison leads to rationalize the emergence of spirals in terms of a rotational invariance at the coarse-grained level, and to elucidate the role of hydrodynamic fluctuations. △ Less

Submitted 16 December, 2024; v1 submitted 22 October, 2023; originally announced October 2023.

Comments: 7+11 pages, 4+4 figures

Active matter under control: Insights from response theory

Authors: Luke K. Davis, Karel Proesmans, Étienne Fodor

Abstract: Active constituents burn fuel to sustain individual motion, giving rise to collective effects that are not seen in systems at thermal equilibrium, such as phase separation with purely repulsive interactions. There is a great potential in harnessing the striking phenomenology of active matter to build novel controllable and responsive materials that surpass passive ones. Yet, we currently lack a sy… ▽ More Active constituents burn fuel to sustain individual motion, giving rise to collective effects that are not seen in systems at thermal equilibrium, such as phase separation with purely repulsive interactions. There is a great potential in harnessing the striking phenomenology of active matter to build novel controllable and responsive materials that surpass passive ones. Yet, we currently lack a systematic roadmap to predict the protocols driving active systems between different states in a way that is thermodynamically optimal. Equilibrium thermodynamics is an inadequate foundation to this end, due to the dissipation rate arising from the constant fuel consumption in active matter. Here, we derive and implement a versatile framework for the thermodynamic control of active matter. Combining recent developments in stochastic thermodynamics and nonequilibrium response theory, our approach shows how to find the optimal control for either continuous- or discrete-state active systems operating arbitrarily far from equilibrium. Our results open the door to designing novel active materials which are not only built to stabilize specific nonequilibrium collective states, but are also optimized to switch between different states at minimum dissipation. △ Less

Submitted 15 February, 2024; v1 submitted 18 May, 2023; originally announced May 2023.

Journal ref: Phys. Rev. X 14, 011012 (2024)

Nonideal Reaction-Diffusion Systems: Multiple Routes to Instability

Authors: Timur Aslyamov, Francesco Avanzini, Étienne Fodor, Massimiliano Esposito

Abstract: We develop a general classification of the nature of the instabilities yielding spatial organization in open nonideal reaction-diffusion systems, based on linear stability analysis. This encompasses dynamics where chemical species diffuse, interact with each other, and undergo chemical reactions driven out of equilibrium by external chemostats. We find analytically that these instabilities can be… ▽ More We develop a general classification of the nature of the instabilities yielding spatial organization in open nonideal reaction-diffusion systems, based on linear stability analysis. This encompasses dynamics where chemical species diffuse, interact with each other, and undergo chemical reactions driven out of equilibrium by external chemostats. We find analytically that these instabilities can be of two types: instabilities caused by intermolecular energetic interactions (E type), and instabilities caused by multimolecular out-of-equilibrium chemical reactions (R type). Furthermore, we identify a class of chemical reaction networks, containing unimolecular networks but also extending beyond them, that can only undergo E-type instabilities. We illustrate our analytical findings with numerical simulations on two reaction-diffusion models, each displaying one of the two types of instability and generating stable patterns. △ Less

Submitted 4 October, 2023; v1 submitted 13 April, 2023; originally announced April 2023.

Journal ref: Phys. Rev. Lett. 131, 138301, 2023

Towards a liquid-state theory for active matter

Authors: Yuting Irene Li, Rosalba Garcia-Millan, Michael E. Cates, Étienne Fodor

Abstract: In equilibrium, the collective behaviour of particles interacting via steep, short-ranged potentials is well captured by the virial expansion of the free energy at low density. Here, we extend this approach beyond equilibrium to the case of active matter with self-propelled particles. Given that active systems do not admit any free-energy description in general, our aim is to build the dynamics of… ▽ More In equilibrium, the collective behaviour of particles interacting via steep, short-ranged potentials is well captured by the virial expansion of the free energy at low density. Here, we extend this approach beyond equilibrium to the case of active matter with self-propelled particles. Given that active systems do not admit any free-energy description in general, our aim is to build the dynamics of the coarse-grained density from first principles without any equilibrium assumption. Starting from microscopic equations of motion, we obtain the hierarchy of density correlations, which we close with an ansatz for the two-point density valid in the dilute regime at small activity. This closure yields the nonlinear dynamics of the one-point density, with hydrodynamic coefficients depending explicitly on microscopic interactions, by analogy with the equilibrium virial expansion. This dynamics admits a spinodal instability for purely repulsive interactions, a signature of motility-induced phase separation. Therefore, although our approach should be restricted to dilute, weakly-active systems a priori, it actually captures the features of a broader class of active matter. △ Less

Submitted 24 May, 2023; v1 submitted 28 January, 2023; originally announced January 2023.

Comments: 2 figures

Journal ref: EPL 142, 57004 (2023)

Pulsating active matter

Authors: Yiwei Zhang, Étienne Fodor

Abstract: We reveal that the mechanical pulsation of locally synchronised particles is a generic route to propagate deformation waves. We consider a model of dense repulsive particles whose activity drives periodic change in size of each individual. The dynamics is inspired by biological tissues where cells consume fuel to sustain active deformation. We show that the competition between repulsion and synchr… ▽ More We reveal that the mechanical pulsation of locally synchronised particles is a generic route to propagate deformation waves. We consider a model of dense repulsive particles whose activity drives periodic change in size of each individual. The dynamics is inspired by biological tissues where cells consume fuel to sustain active deformation. We show that the competition between repulsion and synchronisation triggers an instability which promotes a wealth of dynamical patterns, ranging from spiral waves to defect turbulence. We identify the mechanisms underlying the emergence of patterns, and characterize the corresponding transitions. By coarse-graining the dynamics, we propose a hydrodynamic description of an assembly of pulsating particles, and discuss an analogy with reaction-diffusion systems. △ Less

Submitted 9 December, 2023; v1 submitted 14 August, 2022; originally announced August 2022.

Comments: 6 pages, 4 figures

Journal ref: Phys. Rev. Lett. 131, 238302 (2023)

Mean-field theory for the structure of strongly interacting active liquids

Authors: Laura Tociu, Gregory Rassolov, Étienne Fodor, Suriyanarayanan Vaikuntanathan

Abstract: Active systems, which are driven out of equilibrium by local non-conservative forces, exhibit unique behaviors and structures with potential utility for the design of novel materials. An important and difficult challenge along the path towards this goal is to precisely predict how the structure of active systems is modified as their driving forces push them out of equilibrium. Here, we use tools f… ▽ More Active systems, which are driven out of equilibrium by local non-conservative forces, exhibit unique behaviors and structures with potential utility for the design of novel materials. An important and difficult challenge along the path towards this goal is to precisely predict how the structure of active systems is modified as their driving forces push them out of equilibrium. Here, we use tools from liquid-state theories to approach this challenge for a classic minimal active matter model. First, we construct a nonequilibrium mean-field framework which can predict the structure of systems of weakly interacting particles. Second, motivated by equilibrium solvation theories, we modify this theory to extend it with surprisingly high accuracy to systems of strongly interacting particles, distinguishing it from most existing similarly tractable approaches. Our results provide insight into spatial organization in strongly interacting out-of-equilibrium systems. △ Less

Submitted 7 August, 2022; originally announced August 2022.

Comments: 7 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2012.10441

Journal ref: J. Chem. Phys. 157, 014902 (2022)

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

Authors: Michael E. Cates, Étienne Fodor, Tomer Markovich, Cesare Nardini, Elsen Tjhung

Abstract: Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff -- which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction o… ▽ More Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff -- which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing for simplicity on models with a purely diffusive scalar field, such as `Model B' which describes phase separation in binary fluid mixtures. We address the requirement that the steady state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for `active field theories' in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR) we must make a careful treatment of so-called `spurious drift' and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative, via off-diagonal couplings to additional fields that encode thermodynamically the underlying chemical processes responsible for activity. In this case the spurious drift terms need careful accounting, not just to evaluate correctly the EPR, but also to numerically implement the Langevin dynamics itself. △ Less

Submitted 11 February, 2022; v1 submitted 17 November, 2021; originally announced November 2021.

Comments: 27 pages, 4 figures

Journal ref: Entropy 24, 254 (2022)

Thermodynamic Control of Activity Patterns in Cytoskeletal Networks

Authors: Alexandra Lamtyugina, Yuqing Qiu, Étienne Fodor, Aaron R. Dinner, Suriyanarayanan Vaikuntanathan

Abstract: We aim to identify the control principles governing the adaptable formation of non-equilibrium structures in actomyosin networks. We build a phenomenological model and predict that biasing the energy dissipated by molecular motors should effectively renormalize the motor-mediated interactions between actin filaments. Indeed, using methods from large deviation theory, we demonstrate that biasing en… ▽ More We aim to identify the control principles governing the adaptable formation of non-equilibrium structures in actomyosin networks. We build a phenomenological model and predict that biasing the energy dissipated by molecular motors should effectively renormalize the motor-mediated interactions between actin filaments. Indeed, using methods from large deviation theory, we demonstrate that biasing energy dissipation is equivalent to modulating the motor rigidity and results in an aster-to-bundle transition. From the simulation statistics, we extract a relation between the biasing parameter and the corresponding normalized motor rigidity. This work elucidates the relationship between energy dissipation, effective interactions, and pattern formation in active biopolymer networks, providing a control principle of cytoskeletal structure and dynamics. △ Less

Submitted 26 September, 2022; v1 submitted 16 November, 2021; originally announced November 2021.

Comments: 6 pages, 2 figures

Journal ref: Phys. Rev. Lett. 129, 128002 (2022)

Optimal power and efficiency of odd engines

Authors: Étienne Fodor, Anton Souslov

Abstract: Odd materials feature antisymmetric response to perturbations. This anomalous property can stem from the nonequilibrium activity of their components, which is sustained by an external energy supply. These materials open the door to designing innovative engines which extract work by applying cyclic deformations, without any equivalent in equilibrium. Here, we reveal that the efficiency of such ener… ▽ More Odd materials feature antisymmetric response to perturbations. This anomalous property can stem from the nonequilibrium activity of their components, which is sustained by an external energy supply. These materials open the door to designing innovative engines which extract work by applying cyclic deformations, without any equivalent in equilibrium. Here, we reveal that the efficiency of such energy conversion, from local activity to macroscopic work, can be arbitrarily close to unity when the cycles of deformation are properly designed. We illustrate these principles in some canonical viscoelastic materials, which leads us to identify strategies for optimizing power and efficiency according to material properties, and to delineate guidelines for the design of more complex odd engines. △ Less

Submitted 30 December, 2021; v1 submitted 22 September, 2021; originally announced September 2021.

Comments: 6 pages, 2 figures

Journal ref: Phys. Rev. E 104, L062602 (2021)

Power fluctuations in sheared amorphous materials: A minimal model

Authors: Timothy Ekeh, Étienne Fodor, Suzanne M. Fielding, Michael E. Cates

Abstract: The importance of mesoscale fluctuations in flowing amorphous materials is widely accepted, without a clear understanding of their role. We propose a mean-field elastoplastic model that admits both stress and strain-rate fluctuations, and investigate the character of its power distribution under steady shear flow. The model predicts the suppression of negative power fluctuations near the liquid-so… ▽ More The importance of mesoscale fluctuations in flowing amorphous materials is widely accepted, without a clear understanding of their role. We propose a mean-field elastoplastic model that admits both stress and strain-rate fluctuations, and investigate the character of its power distribution under steady shear flow. The model predicts the suppression of negative power fluctuations near the liquid-solid transition; the existence of a fluctuation relation in limiting regimes but its replacement in general by stretched-exponential power-distribution tails; and a crossover between two distinct mechanisms for negative power fluctuations in the liquid and the yielding solid phases. We connect these predictions with recent results from particle-based, numerical micro-rheological experiments. △ Less

Submitted 24 June, 2021; originally announced June 2021.

Comments: 11 pages, 4 figures

Journal ref: Phys. Rev. E 105, L052601 (2022)

Irreversibility and biased ensembles in active matter: Insights from stochastic thermodynamics

Authors: Étienne Fodor, Robert L. Jack, Michael E. Cates

Abstract: Active systems evade the rules of equilibrium thermodynamics by constantly dissipating energy at the level of their microscopic components. This energy flux stems from the conversion of a fuel, present in the environment, into sustained individual motion. It can lead to collective effects without any equilibrium equivalent, such as a phase separation for purely repulsive particles, or a collective… ▽ More Active systems evade the rules of equilibrium thermodynamics by constantly dissipating energy at the level of their microscopic components. This energy flux stems from the conversion of a fuel, present in the environment, into sustained individual motion. It can lead to collective effects without any equilibrium equivalent, such as a phase separation for purely repulsive particles, or a collective motion (flocking) for aligning particles. Some of these effects can be rationalized by using equilibrium tools to recapitulate nonequilibrium transitions. An important challenge is then to delineate systematically to which extent the character of these active transitions is genuinely distinct from equilibrium analogs. We review recent works that use stochastic thermodynamics tools to identify, for active systems, a measure of irreversibility comprising a coarse-grained or informatic entropy production. We describe how this relates to the underlying energy dissipation or thermodynamic entropy production, and how it is influenced by collective behavior. Then, we review the possibility to construct thermodynamic ensembles out-of-equilibrium, where trajectories are biased towards atypical values of nonequilibrium observables. We show that this is a generic route to discovering unexpected phase transitions in active matter systems, which can also inform their design. △ Less

Submitted 12 March, 2022; v1 submitted 14 April, 2021; originally announced April 2021.

Comments: 23 pages, 3 figures

Journal ref: Annu. Rev. Condens. Matter Phys 13, 215 (2022)

Active engines: Thermodynamics moves forward

Authors: Étienne Fodor, Michael E. Cates

Abstract: The study of thermal heat engines was pivotal to establishing the principles of equilibrium thermodynamics, with implications far wider than only engine optimization. For nonequilibrium systems, which by definition dissipate energy even at rest, how to best convert such dissipation into useful work is still largely an outstanding question, with similar potential to illuminate general physical prin… ▽ More The study of thermal heat engines was pivotal to establishing the principles of equilibrium thermodynamics, with implications far wider than only engine optimization. For nonequilibrium systems, which by definition dissipate energy even at rest, how to best convert such dissipation into useful work is still largely an outstanding question, with similar potential to illuminate general physical principles. We review recent theoretical progress in studying the performances of engines operating with active matter, where particles are driven by individual self-propulsion. We distinguish two main classes, either autonomous engines exploiting a particle current, or cyclic engines applying periodic transformation to the system, and present the strategies put forward so far for optimization. We delineate the limitations of previous studies, and propose some futures perspectives, with a view to building a consistent thermodynamic framework far from equilibrium. △ Less

Submitted 16 May, 2021; v1 submitted 29 January, 2021; originally announced January 2021.

Comments: 7 pages, 4 figures

Journal ref: EPL 134, 10003 (2021)

From predicting to learning dissipation from pair correlations of active liquids

Authors: Gregory Rassolov, Laura Tociu, Étienne Fodor, Suriyanarayanan Vaikuntanathan

Abstract: Active systems, which are driven out of equilibrium by local non-conservative forces, can adopt unique behaviors and configurations. An important challenge in the design of novel materials which utilize such properties is to precisely connect the static structure of active systems to the dissipation of energy induced by the local driving. Here, we use tools from liquid-state theories and machine l… ▽ More Active systems, which are driven out of equilibrium by local non-conservative forces, can adopt unique behaviors and configurations. An important challenge in the design of novel materials which utilize such properties is to precisely connect the static structure of active systems to the dissipation of energy induced by the local driving. Here, we use tools from liquid-state theories and machine learning to take on this challenge. We first demonstrate analytically for an isotropic active matter system that dissipation and pair correlations are closely related when driving forces behave like an active temperature. We then extend a nonequilibrium mean-field framework for predicting these pair correlations, which unlike most existing approaches is applicable even for strongly interacting particles and far from equilibrium, to predicting dissipation in these systems. Based on this theory, we reveal a robust analytic relation between dissipation and structure which holds even as the system approaches a nonequilibrium phase transition. Finally, we construct a neural network which maps static configurations of particles to their dissipation rate without any prior knowledge of the underlying dynamics. Our results open novel perspectives on the interplay between dissipation and organization out-of-equilibrium. △ Less

Submitted 7 August, 2022; v1 submitted 18 December, 2020; originally announced December 2020.

Comments: 13 pages, 4 figures

Journal ref: J. Chem. Phys. 157, 054901 (2022)

Collective motion in large deviations of active particles

Authors: Yann-Edwin Keta, Étienne Fodor, Frédéric van Wijland, Michael E. Cates, Robert L. Jack

Abstract: We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when the active work is biased towards larger values, and is associated with alignment of particles' orientations. A finite biasing field is needed to induce spontaneo… ▽ More We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when the active work is biased towards larger values, and is associated with alignment of particles' orientations. A finite biasing field is needed to induce spontaneous symmetry breaking, even in large systems. Particle alignment is computed exactly for a system of two particles. For many-particle systems, we analyse the symmetry breaking by an optimal-control representation of the biased dynamics, and we propose a fluctuating hydrodynamic theory that captures the emergence of polar order in the biased state. △ Less

Submitted 15 September, 2020; originally announced September 2020.

Comments: 28 pages

Journal ref: Phys. Rev. E 103, 022603 (2021)

Statistical Mechanics of Active Ornstein Uhlenbeck Particles

Authors: David Martin, Jérémy O'Byrne, Michael E. Cates, Étienne Fodor, Cesare Nardini, Julien Tailleur, Frédéric van Wijland

Abstract: We review and extend recent developments on the statistical properties of Active Ornstein Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffice to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We first detail the perturbative… ▽ More We review and extend recent developments on the statistical properties of Active Ornstein Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffice to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We first detail the perturbative derivation of the steady state of AOUPs in the small persistence time limit. We show the existence of an effective equilibrium regime in which detailed-balance is obeyed with respect to a non-Boltzmann distribution and detail the corresponding fluctuation-dissipation theorem. We then characterize the departure from equilibrium by computing several relevant observables (entropy production, ratchet current). At the collective level, we show AOUPs to experience motility-induced phase separation both in the presence of pairwise forces or due to quorum-sensing interactions. The latter can be accounted for by considering the steady-state of AOUPs with spatially varying propulsion speed or persistence time. Finally, we discuss how the emerging properties of AOUPs can be characterized from the dynamics of their collective modes, which we construct explicitly. △ Less

Submitted 14 July, 2021; v1 submitted 29 August, 2020; originally announced August 2020.

Journal ref: Phys. Rev. E 103, 032607 (2021)

Thermodynamics of active field theories: Energetic cost of coupling to reservoirs

Authors: Tomer Markovich, Étienne Fodor, Elsen Tjhung, Michael E. Cates

Abstract: The hallmark of active matter is the autonomous directed motion of its microscopic constituents driven by consumption of energy resources. This leads to the emergence of large scale dynamics and structures without any equilibrium equivalent. Though active field theories offer a useful hydrodynamic description, it is unclear how to properly quantify the energetic cost of the dynamics from such a co… ▽ More The hallmark of active matter is the autonomous directed motion of its microscopic constituents driven by consumption of energy resources. This leads to the emergence of large scale dynamics and structures without any equilibrium equivalent. Though active field theories offer a useful hydrodynamic description, it is unclear how to properly quantify the energetic cost of the dynamics from such a coarse-grained description. We provide a thermodynamically consistent framework to identify the energy exchanges between active systems and their surrounding thermostat at the hydrodynamic level. Based on linear irreversible thermodynamics, we determine how active fields couple with the underlying reservoirs at the basis of nonequilibrium driving. This leads to evaluating the rate of heat dissipated in the thermostat, as a measure of the cost to sustain the system away from equilibrium, which is related to the irreversibility of the active field dynamics. We demonstrate the applicability of our approach in two popular active field theories: (i) the dynamics of a conserved density field reproducing active phase separation, and (ii) the coupled dynamics of density and polarization describing motile deformable droplets. Combining numerical and analytical approaches, we provide spatial maps of dissipated heat, compare them with the irreversibility measure of the active field dynamics, and explore how the overall dissipated heat varies with the emerging order. △ Less

Submitted 19 June, 2021; v1 submitted 15 August, 2020; originally announced August 2020.

Comments: 23 pages, 7 figures

Journal ref: Phys. Rev. X 11, 021057 (2021)

Time-reversal symmetry violations and entropy production in field theories of polar active matter

Authors: Øyvind L. Borthne, Étienne Fodor, Michael E. Cates

Abstract: We investigate the steady-state entropy production rate (EPR) in the Hydrodynamic Vicsek Model (HVM) and Diffusive Flocking Model (DFM). Both models display a transition from an isotropic gas to a polar liquid (flocking) phase, in addition to traveling polar clusters and microphase-separation in the miscibility gap. The phase diagram of the DFM, which may be considered an extension of the HVM, con… ▽ More We investigate the steady-state entropy production rate (EPR) in the Hydrodynamic Vicsek Model (HVM) and Diffusive Flocking Model (DFM). Both models display a transition from an isotropic gas to a polar liquid (flocking) phase, in addition to traveling polar clusters and microphase-separation in the miscibility gap. The phase diagram of the DFM, which may be considered an extension of the HVM, contains additional structure at low densities where we find a novel crystal phase in which a stationary hexagonal lattice of high-density ridges surround low density valleys. From an assessment of the scaling of the EPR at low noise, we uncover that the dynamics in this limit may be organised into three main classes based on the dominant contribution. Truly nonequilibrium dynamics is characterised by a divergent EPR in this limit, and sustains global time-reversal symmetry (TRS) violating currents at zero noise. On the other hand, marginally nonequilibrium and effectively equilibrium dynamics have a finite EPR in this limit, and TRS is broken only at the level of fluctuations. For the latter of these two cases, detailed balance is restored in the small noise limit and we recover effective Boltzmann statistics to lowest nontrivial order. We further demonstrate that the scaling of the EPR may change depending on the dynamical variables that are tracked when it is computed, and the protocol chosen for time-reversal. Results acquired from numerical simulations of the dynamics confirm both the asymptotic scaling relations we derive and our quantitative predictions. △ Less

Submitted 18 December, 2020; v1 submitted 5 August, 2020; originally announced August 2020.

Journal ref: New J. Phys. 22, 123012 (2020)

Thermodynamic cycles with active matter

Authors: Timothy Ekeh, Michael E. Cates, Étienne Fodor

Abstract: Active matter constantly dissipates energy to power the self-propulsion of its microscopic constituents. This opens the door to designing innovative cyclic engines without any equilibrium equivalent. We offer a consistent thermodynamic framework to characterize and optimize the performances of such cycles. Based on a minimal model, we put forward a protocol which extracts work by controlling only… ▽ More Active matter constantly dissipates energy to power the self-propulsion of its microscopic constituents. This opens the door to designing innovative cyclic engines without any equilibrium equivalent. We offer a consistent thermodynamic framework to characterize and optimize the performances of such cycles. Based on a minimal model, we put forward a protocol which extracts work by controlling only the properties of the confining walls at boundaries, and we rationalize the transitions between optimal cycles. We show that the corresponding power and efficiency are generally proportional, so that they reach their maximum values at same cycle time in contrast with thermal cycles, and we provide a generic relation constraining the fluctuations of the power. △ Less

Submitted 1 July, 2020; v1 submitted 14 February, 2020; originally announced February 2020.

Comments: 7 pages, 3 figures

Journal ref: Phys. Rev. E 102, 010101 (2020)

Dissipation controls transport and phase transitions in active fluids: Mobility, diffusion and biased ensembles

Authors: Étienne Fodor, Takahiro Nemoto, Suriyanarayanan Vaikuntanathan

Abstract: Active fluids operate by constantly dissipating energy at the particle level to perform a directed motion, yielding dynamics and phases without any equilibrium equivalent. The emerging behaviors have been studied extensively, yet deciphering how local energy fluxes control the collective phenomena is still largely an open challenge. We provide generic relations between the activity-induced dissipa… ▽ More Active fluids operate by constantly dissipating energy at the particle level to perform a directed motion, yielding dynamics and phases without any equilibrium equivalent. The emerging behaviors have been studied extensively, yet deciphering how local energy fluxes control the collective phenomena is still largely an open challenge. We provide generic relations between the activity-induced dissipation and the transport properties of an internal tracer. By exploiting a mapping between active fluctuations and disordered driving, our results reveal how the local dissipation, at the basis of self-propulsion, constrains internal transport by reducing the mobility and the diffusion of particles. Then, we employ techniques of large deviations to investigate how interactions are affected when varying dissipation. This leads us to shed light on a microscopic mechanism to promote clustering at low dissipation, and we also show the existence of collective motion at high dissipation. Overall, these results illustrate how tuning dissipation provides an alternative route to phase transitions in active fluids. △ Less

Submitted 31 January, 2020; v1 submitted 9 September, 2019; originally announced September 2019.

Comments: 26 pages, 7 figures

Journal ref: New J. Phys. 22, 013052 (2020)

Autonomous engines driven by active matter: Energetics and design principles

Authors: Patrick Pietzonka, Étienne Fodor, Christoph Lohrmann, Michael E. Cates, Udo Seifert

Abstract: Because of its nonequilibrium character, active matter in a steady state can drive engines that autonomously deliver work against a constant mechanical force or torque. As a generic model for such an engine, we consider systems that contain one or several active components and a single passive one that is asymmetric in its geometrical shape or its interactions. Generally, one expects that such an… ▽ More Because of its nonequilibrium character, active matter in a steady state can drive engines that autonomously deliver work against a constant mechanical force or torque. As a generic model for such an engine, we consider systems that contain one or several active components and a single passive one that is asymmetric in its geometrical shape or its interactions. Generally, one expects that such an asymmetry leads to a persistent, directed current in the passive component, which can be used for the extraction of work. We validate this expectation for a minimal model consisting of an active and a passive particle on a one-dimensional lattice. It leads us to identify thermodynamically consistent measures for the efficiency of the conversion of isotropic activity to directed work. For systems with continuous degrees of freedom, work cannot be extracted using a one-dimensional geometry under quite general conditions. In contrast, we put forward two-dimensional shapes of a movable passive obstacle that are best suited for the extraction of work, which we compare with analytical results for an idealised work-extraction mechanism. For a setting with many noninteracting active particles, we use a mean-field approach to calculate the power and the efficiency, which we validate by simulations. Surprisingly, this approach reveals that the interaction with the passive obstacle can mediate cooperativity between otherwise noninteracting active particles, which enhances the extracted power per active particle significantly. △ Less

Submitted 14 November, 2019; v1 submitted 1 May, 2019; originally announced May 2019.

Comments: 21 pages, 8 figures

Journal ref: Phys. Rev. X 9, 041032 (2019)

Driven probe under harmonic confinement in a colloidal bath

Authors: Vincent Démery, Étienne Fodor

Abstract: Colloids held by optical or magnetic tweezers have been used to explore the local rheological properties of a complex medium and to extract work from fluctuations with some appropriate protocols. However, a general theoretical understanding of the interplay between the confinement and the interaction with the environment is still lacking. Here, we explore the statistical properties of the position… ▽ More Colloids held by optical or magnetic tweezers have been used to explore the local rheological properties of a complex medium and to extract work from fluctuations with some appropriate protocols. However, a general theoretical understanding of the interplay between the confinement and the interaction with the environment is still lacking. Here, we explore the statistical properties of the position of a probe confined in a harmonic trap moving at constant velocity and interacting with a bath of colloidal particles maintained at a different temperature. Interactions among particles are accounted for by a systematic perturbation, whose range of validity is tested against direct simulations of the full dynamics. Overall, our results provide a way to predict the effect of the driving and the environment on the probe, and can potentially be used to investigate the properties of colloidal heat engines with many-body interactions. △ Less

Submitted 14 January, 2019; v1 submitted 23 November, 2018; originally announced November 2018.

Comments: 17 pages, 4 figures

Journal ref: J. Stat. Mech. 033202 (2019)

Non-Gaussian noise without memory in active matter

Authors: Étienne Fodor, Hisao Hayakawa, Julien Tailleur, Frédéric van Wijland

Abstract: Modeling the dynamics of an individual active particle invariably involves an isotropic noisy self-propulsion component, in the form of run-and-tumble motion or variations around it. This nonequilibrium source of noise is neither white---there is persistence---nor Gaussian. While emerging collective behavior in active matter has hitherto been attributed to the persistent ingredient, we focus on th… ▽ More Modeling the dynamics of an individual active particle invariably involves an isotropic noisy self-propulsion component, in the form of run-and-tumble motion or variations around it. This nonequilibrium source of noise is neither white---there is persistence---nor Gaussian. While emerging collective behavior in active matter has hitherto been attributed to the persistent ingredient, we focus on the non-Gaussian ingredient of self-propulsion. We show that by itself, that is without invoking any memory effect, it is able to generate particle accumulation close to boundaries and effective attraction between otherwise repulsive particles, a mechanism which generically leads to motility-induced phase separation in active matter. △ Less

Submitted 22 November, 2018; v1 submitted 27 September, 2018; originally announced September 2018.

Comments: 14 pages, 4 figures

Journal ref: Phys. Rev. E 98, 062610 (2018)

How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure and biased interactions

Authors: Laura Tociu, Étienne Fodor, Takahiro Nemoto, Suriyanarayanan Vaikuntanathan

Abstract: The dynamics and structure of nonequilibrium liquids, driven by non-conservative forces which can be either external or internal, generically hold the signature of the net dissipation of energy in the thermostat. Yet, disentangling precisely how dissipation changes collective effects remains challenging in many-body systems due to the complex interplay between driving and particle interactions. Fi… ▽ More The dynamics and structure of nonequilibrium liquids, driven by non-conservative forces which can be either external or internal, generically hold the signature of the net dissipation of energy in the thermostat. Yet, disentangling precisely how dissipation changes collective effects remains challenging in many-body systems due to the complex interplay between driving and particle interactions. First, we combine explicit coarse-graining and stochastic calculus to obtain simple relations between diffusion, density correlations and dissipation in nonequilibrium liquids. Based on these results, we consider large-deviation biased ensembles where trajectories mimic the effect of an external drive. The choice of the biasing function is informed by the connection between dissipation and structure derived in the first part. Using analytical and computational techniques, we show that biasing trajectories effectively renormalizes interactions in a controlled manner, thus providing intuition on how driving forces can lead to spatial organization and collective dynamics. Altogether, our results show how tuning dissipation provides a route to alter the structure and dynamics of liquids and soft materials. △ Less

Submitted 16 October, 2019; v1 submitted 23 August, 2018; originally announced August 2018.

Comments: 21 pages, 7 figures

Journal ref: Phys. Rev. X 9, 041026 (2019)

Optimizing active work: Dynamical phase transitions, collective motion, and jamming

Authors: Takahiro Nemoto, Étienne Fodor, Michael E. Cates, Robert L. Jack, Julien Tailleur

Abstract: Active work measures how far the local self-forcing of active particles translates into real motion. Using Population Monte Carlo methods, we investigate large deviations in the active work for repulsive active Brownian disks. Minimizing the active work generically results in dynamical arrest; in contrast, despite the lack of aligning interactions, trajectories of high active work correspond to a… ▽ More Active work measures how far the local self-forcing of active particles translates into real motion. Using Population Monte Carlo methods, we investigate large deviations in the active work for repulsive active Brownian disks. Minimizing the active work generically results in dynamical arrest; in contrast, despite the lack of aligning interactions, trajectories of high active work correspond to a collectively moving, aligned state. We use heuristic and analytic arguments to explain the origin of dynamical phase transitions separating the arrested, typical, and aligned regimes. △ Less

Submitted 9 February, 2019; v1 submitted 8 May, 2018; originally announced May 2018.

Comments: 14 pages, 9 figures

Journal ref: Phys. Rev. E 99, 022605 (2019)

Extracting maximum power from active colloidal heat engines

Authors: D. Martin, C. Nardini, M. E. Cates, É. Fodor

Abstract: Colloidal heat engines extract power out of a fluctuating bath by manipulating a confined tracer. Considering a self-propelled tracer surrounded by a bath of passive colloids, we optimize the engine performances based on the maximum available power. Our approach relies on an adiabatic mean-field treatment of the bath particles which reduces the many-body description into an effective tracer dynami… ▽ More Colloidal heat engines extract power out of a fluctuating bath by manipulating a confined tracer. Considering a self-propelled tracer surrounded by a bath of passive colloids, we optimize the engine performances based on the maximum available power. Our approach relies on an adiabatic mean-field treatment of the bath particles which reduces the many-body description into an effective tracer dynamics. It leads us to reveal that, when operated at constant activity, an engine can only produce less maximum power than its passive counterpart. In contrast, the output power of an isothermal engine, operating with cyclic variations of the self-propulsion without any passive equivalent, exhibits an optimum in terms of confinement and activity. Direct numerical simulations of the microscopic dynamics support the validity of these results even beyond the mean-field regime, with potential relevance to the design of experimental engines. △ Less

Submitted 23 April, 2018; v1 submitted 5 March, 2018; originally announced March 2018.

Comments: 7 pages, 2 figures

Journal ref: EPL 121, 60005 (2018)

The statistical physics of active matter: from self-catalytic colloids to living cells

Authors: Étienne Fodor, M. Cristina Marchetti

Abstract: These lecture notes are designed to provide a brief introduction into the phenomenology of active matter and to present some of the analytical tools used to rationalize the emergent behavior of active systems. Such systems are made of interacting agents able to extract energy stored in the environment to produce sustained directed motion. The local conversion of energy into mechanical work drives… ▽ More These lecture notes are designed to provide a brief introduction into the phenomenology of active matter and to present some of the analytical tools used to rationalize the emergent behavior of active systems. Such systems are made of interacting agents able to extract energy stored in the environment to produce sustained directed motion. The local conversion of energy into mechanical work drives the system far from equilibrium, yielding new dynamics and phases. The emerging phenomena can be classified depending on the symmetry of the active particles and on the type of microscopic interactions. We focus here on steric and aligning interactions, as well as interactions driven by shape changes. The models that we present are all inspired by experimental realizations of either synthetic, biomimetic or living systems. Based on minimal ingredients, they are meant to bring a simple and synthetic understanding of the complex phenomenology of active matter. △ Less

Submitted 21 December, 2017; v1 submitted 29 August, 2017; originally announced August 2017.

Comments: Lecture notes for the international summer school "Fundamental Problems in Statistical Physics" 2017 in Bruneck

Journal ref: Physica A 504, 106 (2018)

Entropy production in field theories without time reversal symmetry: Quantifying the non-equilibrium character of active matter

Authors: Cesare Nardini, Etienne Fodor, Elsen Tjhung, Frederic van Wijland, Julien Tailleur, Michael E. Cates

Abstract: Active matter systems operate far from equilibrium due to the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the probability ratio of forward and reversed dynamics and hence the importance of irreversibility at such scales: it vanishes whenever the coarse-grained dynamics of th… ▽ More Active matter systems operate far from equilibrium due to the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the probability ratio of forward and reversed dynamics and hence the importance of irreversibility at such scales: it vanishes whenever the coarse-grained dynamics of the active system reduces to that of an effective equilibrium model. We evaluate S for a class of scalar stochastic field theories describing the coarse-grained density of self-propelled particles without alignment interactions, capturing such key phenomena as motility-induced phase separation. We show how the entropy production can be decomposed locally (in real space) or spectrally (in Fourier space), allowing detailed examination of the spatial structure and correlations that underly departures from equilibrium. For phase-separated systems, the local entropy production is concentrated mainly on interfaces with a bulk contribution that tends to zero in the weak-noise limit. In homogeneous states, we find a generalized Harada-Sasa relation that directly expresses the entropy production in terms of the wavevector-dependent deviation from the fluctuation-dissipation relation between response functions and correlators. We discuss extensions to the case where the particle density is coupled to a momentum-conserving solvent, and to situations where the particle current, rather than the density, should be chosen as the dynamical field. We expect the new conceptual tools developed here to be broadly useful in the context of active matter, allowing one to distinguish when and where activity plays an essential role in the dynamics. △ Less

Submitted 23 April, 2017; v1 submitted 19 October, 2016; originally announced October 2016.

Journal ref: Phys. Rev. X 7, 021007 (2017)

How far from equilibrium is active matter?

Authors: Étienne Fodor, Cesare Nardini, Mike E. Cates, Julien Tailleur, Paolo Visco, Frédéric van Wijland

Abstract: Active matter systems are driven out of thermal equilibrium by a lack of generalized Stokes-Einstein relation between injection and dissipation of energy at the microscopic scale. We consider such a system of interacting particles, propelled by persistent noises, and show that, at small but finite persistence time, their dynamics still satisfy a time-reversal symmetry. To do so, we compute perturb… ▽ More Active matter systems are driven out of thermal equilibrium by a lack of generalized Stokes-Einstein relation between injection and dissipation of energy at the microscopic scale. We consider such a system of interacting particles, propelled by persistent noises, and show that, at small but finite persistence time, their dynamics still satisfy a time-reversal symmetry. To do so, we compute perturbatively their steady-state measure and show that, for short persistent times, the entropy production rate vanishes. This endows such systems with an effective Fluctuation-Dissipation theorem akin to that of thermal equilibrium systems. Last we show how interacting particle systems with viscous drags and correlated noises can be seen as in equilibrium with a visco-elastic bath but driven out of equilibrium by non-conservative forces, hence providing an energetic insight on the departure of active systems from equilibrium. △ Less

Submitted 4 April, 2016; originally announced April 2016.

Comments: 5 pages, 2 figures

Journal ref: Phys. Rev. Lett. 117, 038103 (2016)

Active cage model of glassy dynamics

Authors: Étienne Fodor, Hisao Hayakawa, Paolo Visco, Frédéric van Wijland

Abstract: We build up a phenomenological picture in terms of the effective dynamics of a tracer confined in a cage experiencing random hops to capture somec haracteristics of glassy systems. This minimal description exhibits scale invariance properties for the small-displacement distribution that echo experimental observations. We predict the existence of exponential tails as a cross-over between two Gaussi… ▽ More We build up a phenomenological picture in terms of the effective dynamics of a tracer confined in a cage experiencing random hops to capture somec haracteristics of glassy systems. This minimal description exhibits scale invariance properties for the small-displacement distribution that echo experimental observations. We predict the existence of exponential tails as a cross-over between two Gaussian regimes. Moreover, we demonstrate that the onset of glassy behavior is controlled only by two dimensionless numbers: the number of hops occurring during the relaxation of the particle within a local cage, and the ratio of the hopping length to the cage size. △ Less

Submitted 17 June, 2016; v1 submitted 25 January, 2016; originally announced January 2016.

Comments: 9 pages, 3 figures

Journal ref: Phys. Rev. E 94, 012610 (2016)

Spatial fluctuations at vertices of epithelial layers: quantification of regulation by Rho pathway

Authors: É. Fodor, V. Mehandia, J. Comelles, R. Thiagarajan, N. S. Gov, P. Visco, F. van Wijland, D. Riveline

Abstract: In living matter, shape fluctuations induced by acto-myosin are usually studied in vitro via reconstituted gels, whose properties are controlled by changing the concentrations of actin, myosin and cross-linkers. Such an approach deliberately avoids to consider the complexity of biochemical signaling inherent to living systems. Acto-myosin activity inside living cells is mainly regulated by the Rho… ▽ More In living matter, shape fluctuations induced by acto-myosin are usually studied in vitro via reconstituted gels, whose properties are controlled by changing the concentrations of actin, myosin and cross-linkers. Such an approach deliberately avoids to consider the complexity of biochemical signaling inherent to living systems. Acto-myosin activity inside living cells is mainly regulated by the Rho signaling pathway which is composed of multiple layers of coupled activators and inhibitors. We investigate how such a pathway controls the dynamics of confluent epithelial tissues by tracking the displacements of the junction points between cells. Using a phenomenological model to analyze the vertex fluctuations, we rationalize the effects of different Rho signaling targets on the emergent tissue activity by quantifying the effective diffusion coefficient, the persistence time and persistence length of the fluctuations. Our results reveal an unanticipated correlation between layers of activation/inhibition and spatial fluctuations within tissues. Overall, this work connects the regulation via biochemical signaling with mesoscopic spatial fluctuations, with potential application to the study of structural rearrangements in epithelial tissues. △ Less

Submitted 6 February, 2018; v1 submitted 4 December, 2015; originally announced December 2015.

Comments: 8 pages, 3 figures

Journal ref: Biophys. J. 114, 939 (2018)

Nonequilibrium dissipation in living oocytes

Authors: Étienne Fodor, Wylie W. Ahmed, Maria Almonacid, Matthias Bussonnier, Nir S. Gov, Marie-Hélène Verlhac, Timo Betz, Paolo Visco, Frédéric van Wijland

Abstract: Living organisms are inherently out-of-equilibrium systems. We employ new developments in stochastic energetics and rely on a minimal microscopic model to predict the amount of mechanical energy dissipated by such dynamics. Our model includes complex rheological effects and nonequilibrium stochastic forces. By performing active microrheology and tracking micron-sized vesicles in the cytoplasm of l… ▽ More Living organisms are inherently out-of-equilibrium systems. We employ new developments in stochastic energetics and rely on a minimal microscopic model to predict the amount of mechanical energy dissipated by such dynamics. Our model includes complex rheological effects and nonequilibrium stochastic forces. By performing active microrheology and tracking micron-sized vesicles in the cytoplasm of living oocytes, we provide unprecedented measurements of the spectrum of dissipated energy. We show that our model is fully consistent with the experimental data, and we use it to offer predictions for the injection and dissipation energy scales involved in active fluctuations. △ Less

Submitted 22 December, 2016; v1 submitted 3 November, 2015; originally announced November 2015.

Comments: 5 pages, 2 figures

Journal ref: EPL 116, 30008 (2016)

Active mechanics reveal molecular-scale force kinetics in living oocytes

Authors: Wylie W. Ahmed, Etienne Fodor, Maria Almonacid, Matthias Bussonnier, Marie-Helene Verlhac, Nir S. Gov, Paolo Visco, Frederic van Wijland, Timo Betz

Abstract: Active diffusion of intracellular components is emerging as an important process in cell biology. This process is mediated by complex assemblies of molecular motors and cytoskeletal filaments that drive force generation in the cytoplasm and facilitate enhanced motion. The kinetics of molecular motors have been precisely characterized in-vitro by single molecule approaches, however, their in-vivo b… ▽ More Active diffusion of intracellular components is emerging as an important process in cell biology. This process is mediated by complex assemblies of molecular motors and cytoskeletal filaments that drive force generation in the cytoplasm and facilitate enhanced motion. The kinetics of molecular motors have been precisely characterized in-vitro by single molecule approaches, however, their in-vivo behavior remains elusive. Here, we study the active diffusion of vesicles in mouse oocytes, where this process plays a key role in nuclear positioning during development, and combine an experimental and theoretical framework to extract molecular-scale force kinetics (force, power-stroke, and velocity) of the in-vivo active process. Assuming a single dominant process, we find that the nonequilibrium activity induces rapid kicks of duration $τ\sim$ 300 $μ$s resulting in an average force of $F \sim$ 0.4 pN on vesicles in in-vivo oocytes, remarkably similar to the kinetics of in-vitro myosin-V. Our results reveal that measuring in-vivo active fluctuations allows extraction of the molecular-scale activity in agreement with single-molecule studies and demonstrates a mesoscopic framework to access force kinetics. △ Less

Submitted 8 February, 2018; v1 submitted 28 October, 2015; originally announced October 2015.

Comments: 20 pages, 4 figures, see ancillary files for Supplementary Materials, * equally contributing authors

Journal ref: Biophysical Journal 114,7, 1667(2018)

Modeling the dynamics of a tracer particle in an elastic active gel

Authors: E. Ben Isaac, É. Fodor, P. Visco, F. van Wijland, N. S. Gov

Abstract: The internal dynamics of active gels, both in artificial (in-vitro) model systems and inside the cytoskeleton of living cells, has been extensively studied by experiments of recent years. These dynamics are probed using tracer particles embedded in the network of biopolymers together with molecular motors, and distinct non-thermal behavior is observed. We present a theoretical model of the dynamic… ▽ More The internal dynamics of active gels, both in artificial (in-vitro) model systems and inside the cytoskeleton of living cells, has been extensively studied by experiments of recent years. These dynamics are probed using tracer particles embedded in the network of biopolymers together with molecular motors, and distinct non-thermal behavior is observed. We present a theoretical model of the dynamics of a trapped active particle, which allows us to quantify the deviations from equilibrium behavior, using both analytic and numerical calculations. We map the different regimes of dynamics in this system, and highlight the different manifestations of activity: breakdown of the virial theorem and equipartition, different elasticity-dependent "effective temperatures" and distinct non-Gaussian distributions. Our results shed light on puzzling observations in active gel experiments, and provide physical interpretation of existing observations, as well as predictions for future studies. △ Less

Submitted 3 July, 2015; originally announced July 2015.

Comments: 11 pages, 6 figures

Journal ref: Phys. Rev. E 92, 012716 (2015)

Activity driven fluctuations in living cells

Authors: É. Fodor, M. Guo, N. S. Gov, P. Visco, D. A. Weitz, F. van Wijland

Abstract: We propose a model for the dynamics of a probe embedded in a living cell, where both thermal fluctuations and nonequilibrium activity coexist. The model is based on a confining harmonic potential describing the elastic cytoskeletal matrix, which undergoes random active hops as a result of the nonequilibrium rearrangements within the cell. We describe the probe's statistics and we bring forth quant… ▽ More We propose a model for the dynamics of a probe embedded in a living cell, where both thermal fluctuations and nonequilibrium activity coexist. The model is based on a confining harmonic potential describing the elastic cytoskeletal matrix, which undergoes random active hops as a result of the nonequilibrium rearrangements within the cell. We describe the probe's statistics and we bring forth quantities affected by the nonequilibrium activity. We find an excellent agreement between the predictions of our model and experimental results for tracers inside living cells. Finally, we exploit our model to arrive at quantitative predictions for the parameters characterizing nonequilibrium activity, such as the typical time scale of the activity and the amplitude of the active fluctuations. △ Less

Submitted 24 May, 2015; originally announced May 2015.

Comments: 6 pages, 4 figures

Journal ref: EPL 110 48005 (2015)

Generalized Langevin Equation with Hydrodynamic Backflow: Equilibrium Properties

Authors: Étienne Fodor, Denis S. Grebenkov, Paolo Visco, Frédéric van Wijland

Abstract: We review equilibrium properties for the dynamics of a single particle evolving in a visco--elastic medium under the effect of hydrodynamic backflow which includes added mass and Basset force. Arbitrary equilibrium forces acting upon the particle are also included. We discuss the derivation of the explicit expression for the thermal noise correlation function that is consistent with the fluctuatio… ▽ More We review equilibrium properties for the dynamics of a single particle evolving in a visco--elastic medium under the effect of hydrodynamic backflow which includes added mass and Basset force. Arbitrary equilibrium forces acting upon the particle are also included. We discuss the derivation of the explicit expression for the thermal noise correlation function that is consistent with the fluctuation-dissipation theorem. We rely on general time-reversal arguments that apply irrespective of the external potential acting on the particle, but also allow one to retrieve existing results derived for free particles and particles in a harmonic trap. Some consequences for the analysis and interpretation of single-particle tracking experiments are briefly discussed. △ Less

Submitted 10 December, 2014; originally announced December 2014.

Journal ref: Physica A, 422, 107 (2015)

Energetics of active fluctuations in living cells

Authors: Étienne Fodor, Kiyoshi Kanazawa, Hisao Hayakawa, Paolo Visco, Frédéric van Wijland

Abstract: The nonequilibrium activity taking place in a living cell can be monitored with a tracer embedded in the medium. While microrheology experiments based on optical manipulation of such probes have become increasingly standard, we put forward a number of experiments with alternative protocols that, we claim, will provide new insight into the energetics of active fluctuations. These are based on eithe… ▽ More The nonequilibrium activity taking place in a living cell can be monitored with a tracer embedded in the medium. While microrheology experiments based on optical manipulation of such probes have become increasingly standard, we put forward a number of experiments with alternative protocols that, we claim, will provide new insight into the energetics of active fluctuations. These are based on either performing thermodynamic--like cycles in control-parameter space, or on determining response to external perturbations of the confining trap beyond simple translation. We illustrate our proposals on an active itinerant Brownian oscillator modeling the dynamics of a probe embedded in a living medium. △ Less

Submitted 6 June, 2014; originally announced June 2014.

Journal ref: Phys. Rev. E 90, 042724 (2014)