arXiv subjects

Étienne Fodor

Publications and source records attributed to Étienne Fodor.

At least 19 recordsLinked to original sources

arXiv2026

Hydrodynamics of pulsating active liquids

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. 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.

cond-mat.soft↗

arXiv2026

Defect statistics in pulsating active liquids: From contraction waves to aster dynamics

We propose and study a hydrodynamic theory that captures the emergence of contraction waves in dense active liquids composed of pulsating particles subject to isotropic deformation. The coupling between displacement and deformation regulates the interplay between the flow induced by local isotropic deformation and the resistance to pulsation stemming from steric interaction. We reveal that this interplay leads the emergent contraction waves to spontaneously organize into a packing of pacemakers. The relaxation of these pacemakers is governed by a complex feedback between fast and slow aster defects that form in the profiles of velocity flows and of deformation gradients. By mapping contraction waves into these aster defects, we show that such waves adhere to specific constraints, including topological charge conservation and a master curve in the defect velocity statistics, that help rationalize the mechanisms underlying the relaxational dynamics.

cond-mat.stat-mech↗

arXiv2026

Active pistons extract work by periodic compression alone

Active matter is liable to invent protocols that evade the constraints of equilibrium thermodynamics. We put forward active pistons that extract work by periodic compression alone without changing any bulk property of the system. Such pistons necessarily couple the perturbation imposed by an external operator with some degrees of freedom internal to active components. We illustrate this design principle with elastic networks composed of self-aligning motile particles. For slow protocols, self-alignment always overwhelms mechanical friction when the internal activity exceeds a specific threshold controlled by fluctuations. We identify the key response coefficient that helps delineate regimes of work extraction, and reveal that the corresponding phase diagram follows a master curve with re-entrance in terms of noise amplitude. Overall, our active pistons embody a novel design principle with broad implications for building innovative engines far from equilibrium.

cond-mat.soft↗

arXiv2026

Collective deformation of anisotropic particles with internal pulsation

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.

cond-mat.soft↗

arXiv2026

Topology of pulsating active matter: Defect asymmetry controls emergent motility

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.

cond-mat.soft↗

arXiv2026

Irreversibility in scalar active turbulence: The role of topological defects

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.

cond-mat.stat-mech↗

arXiv2025

Control of active field theories at minimal dissipation

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.

cond-mat.stat-mech↗

arXiv2025

Quantifying dissipation in flocking dynamics: When tracking internal states matters

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.

cond-mat.stat-mech↗

arXiv2025

Entropy production rate in thermodynamically consistent flocks

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.

cond-mat.stat-mech↗

arXiv2025

Species interconversion of deformable particles yields transient phase separation

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.

cond-mat.soft↗

arXiv2025

Biased ensembles of pulsating active matter

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.

cond-mat.soft↗

arXiv2024

Diffusive oscillators capture the pulsating states of deformable particles

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.

cond-mat.stat-mech↗

arXiv2024

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

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.

q-bio.MN↗

arXiv2024

Thermodynamically consistent flocking: From discontinuous to continuous transitions

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.

cond-mat.stat-mech↗

arXiv2024

Active matter under control: Insights from response theory

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.

cond-mat.stat-mech↗

arXiv2023

Pulsating active matter

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.

cond-mat.soft↗

arXiv2023

Nonideal Reaction-Diffusion Systems: Multiple Routes to Instability

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.

cond-mat.stat-mech↗

arXiv2023

Towards a liquid-state theory for active matter

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.

cond-mat.soft↗