Lamellar to Micellar Phases and Beyond: When Tactic Active Systems Admit Free Energy Functionals

Unveiling the Phase Diagram and Reaction Paths of the Active Model B with the Deep Minimum Action Method

Nonequilibrium phase transitions are notably difficult to analyze because their mechanisms depend on the system's dynamics in a complex way due to the lack of time-reversal symmetry. To complicate matters, the system's steady-state distribution is unknown in general. Here, the phase diagram of the active Model B is computed with a deep neural network implementation of the geometric minimum action method (gMAM). This approach unveils the unconventional reaction paths and nucleation mechanism in dimensions 1, 2, and 3, by which the system switches between the homogeneous and inhomogeneous phases in the binodal region. Our main findings are (i) the mean time to escape the phase-separated state is (exponentially) extensive in the system size L, but it increases nonmonotonically with L in dimension 1; (ii) the mean time to escape the homogeneous state is always finite, in line with the recent work of Cates and Nardini [Phys. Rev. Lett. 130, 098203 (2023)PRLTAO0031-900710.1103/PhysRevLett.130.098203]; (iii) at fixed L, the active term increases the stability of the homogeneous phase, eventually destroying the phase separation in the binodal for large but finite systems. Our results are particularly relevant for active matter systems in which the number of constituents hardly goes beyond 10^{7} and where finite-size effects matter.

Motility-induced coexistence of a hot liquid and a cold gas

If two phases exist at the same time, such as a gas and a liquid, they have the same temperature. This fundamental law of equilibrium physics is known to apply even to many non-equilibrium systems. However, recently, there has been much attention in the finding that inertial self-propelled particles like Janus colloids in a plasma or microflyers could self-organize into a hot gas-like phase that coexists with a colder liquid-like phase. Here, we show that a kinetic temperature difference across coexisting phases can occur even in equilibrium systems when adding generic (overdamped) self-propelled particles. In particular, we consider mixtures of overdamped active and inertial passive Brownian particles and show that when they phase separate into a dense and a dilute phase, both phases have different kinetic temperatures. Surprisingly, we find that the dense phase (liquid) cannot only be colder but also hotter than the dilute phase (gas). This effect hinges on correlated motions where active particles collectively push and heat up passive ones primarily within the dense phase. Our results answer the fundamental question if a non-equilibrium gas can be colder than a coexisting liquid and create a route to equip matter with self-organized domains of different kinetic temperatures.

Socioeconomic agents as active matter in nonequilibrium Sakoda-Schelling models

How robust are socioeconomic agent-based models with respect to the details of the agents' decision rule? We tackle this question by considering an occupation model in the spirit of the Sakoda-Schelling model, historically introduced to shed light on segregation dynamics among human groups. For a large class of utility functions and decision rules, we pinpoint the nonequilibrium nature of the agent dynamics, while recovering an equilibrium-like phase separation phenomenology. Within the mean-field approximation we show how the model can be mapped, to some extent, onto an active matter field description. Finally, we consider nonreciprocal interactions between two populations and show how they can lead to nonsteady macroscopic behavior. We believe our approach provides a unifying framework to further study geography-dependent agent-based models, notably paving the way for joint consideration of population and price dynamics within a field theoretic approach.

Defect interactions in a two-dimensional sheared lamellar mesophase

The interaction between two edge dislocations in a sheared lyotropic lamellar liquid-crystalline medium is examined. The model is a mesoscale hydrodynamic model based on a free-energy functional that is minimised for a sinusoidal concentration modulation coupled with concentration and momentum equations. The defect dynamics are analysed as a function of the system size and the Ericksen number, the ratio of the shear stress and the characteristic free-energy density for deformation. Three different regimes are observed as the Ericksen number is increased when the edge dislocations are sheared towards each other, such that there is compression of layers between the defects: (a) defect motion that reduces the cross-stream separation till there is a steady spacing with plug flow between the defects, (b) defect attraction and cancellation resulting in a well-aligned state, and (c) defect creation due to a compressional instability between the defects resulting in an increase in the disorder. When the edge dislocations are sheared away from each other, such that there is extension of the layers between the defects, two distinct regimes are observed as the Ericksen number is increased: (a) bending of layers and a plug flow between the defects at their initial separation, and (b) buckling of the layers leading to creation of more defects and a dynamical steady state between defect creation and cancellation. These regimes are found to be robust for different values of the system size, from 32 to 128 layers, and for different values of the dimensionless groups that characterise the ratio of mass/momentum convection and diffusion.

Non-reciprocity across scales in active mixtures

In active matter, particles typically experience mediated interactions, which are not constrained by Newton's third law and are therefore generically non-reciprocal. Non-reciprocity leads to a rich set of emerging behaviors that are hard to account for starting from the microscopic scale, due to the absence of a generic theoretical framework out of equilibrium. Here we consider bacterial mixtures that interact via mediated, non-reciprocal interactions (NRI) like quorum-sensing and chemotaxis. By explicitly relating microscopic and macroscopic dynamics, we show that, under conditions that we derive explicitly, non-reciprocity may fade upon coarse-graining, leading to large-scale equilibrium descriptions. In turn, this allows us to account quantitatively, and without fitting parameters, for the rich behaviors observed in microscopic simulations including phase separation, demixing, and multi-phase coexistence. We also derive the condition under which non-reciprocity survives coarse-graining, leading to a wealth of dynamical patterns. Again, our analytical approach allows us to predict the phase diagram of the system starting from its microscopic description. All in all, our work demonstrates that the fate of non-reciprocity across scales is a subtle and important question.

Arbitrage Equilibrium, Invariance, and the Emergence of Spontaneous Order in the Dynamics of Bird-like Agents

The physics of active biological matter, such as bacterial colonies and bird flocks, exhibiting interesting self-organizing dynamical behavior has gained considerable importance in recent years. Current theoretical advances use techniques from hydrodynamics, kinetic theory, and non-equilibrium statistical physics. However, for biological agents, these approaches do not seem to recognize explicitly their critical feature: namely, the role of survival-driven purpose and the attendant pursuit of maximum utility. Here, we propose a game-theoretic framework, statistical teleodynamics, that demonstrates that the bird-like agents self-organize dynamically into flocks to approach a stable arbitrage equilibriumof equal effective utilities. This is essentially the invisible handmechanism of Adam Smith's in an ecological context. What we demonstrate is for ideal systems, similar to the ideal gas or Ising model in thermodynamics. The next steps would involve examining and learning how real swarms behave compared to their ideal versions. Our theory is not limited to just birds flocking but can be adapted for the self-organizing dynamics of other active matter systems.

The relationship between structure and rheology in a three-dimensional sheared lamellar mesophase

The evolution of a lamellar mesophase from an initially disordered state under shear is examined using simulations of a mesoscale model based on a concentration field ψ that distinguishes the hydrophilic and hydrophobic components. The Landau-Ginzburg free-energy functional is augmented by a term that is minimised for sinusoidal modulations in the concentration field with wavelength λ = (2π/k), and the dynamical equations are the model H equations. The structure and rheology are determined by the relative magnitudes of the diffusion time for coarsening, (λ²/D) and the inverse of the strain rate ^-1, and the Ericksen number, which is the ratio of the shear stress and the layer stiffness. When the diffusion time is small compared with the inverse of the strain rate, there is a local formation of misaligned layers, which are deformed by the imposed flow. There is near-perfect ordering with isolated defects at low values of the Ericksen number, but the defects result in a significant increase in viscosity due to the high layer stiffness. At high values of the Ericksen number, the concentration field is deformed by the mean shear before layers form via diffusion. Cylindrical structures aligned along the flow direction form after about 8-10 strain units, and these evolve into layers with disorder through diffusion perpendicular to the flow. The layers are not perfectly ordered, even after hundreds of strain units, due to the creation and destruction of defects via shear. The excess viscosity is low because the layer stiffness is small compared with the applied shear at a high Ericksen number. This study provides guidance on how the material parameters and imposed flow can be tailored to achieve the desired rheological behaviour.

Nonequilibrium currents in stochastic field theories: A geometric insight

We introduce a formalism to study nonequilibrium steady-state probability currents in stochastic field theories. We show that generalizing the exterior derivative to functional spaces allows identification of the subspaces in which the system undergoes local rotations. In turn, this allows prediction of the counterparts in the real, physical space of these abstract probability currents. The results are presented for the case of the Active Model B undergoing motility-induced phase separation, which is known to be out of equilibrium but whose steady-state currents have not yet been observed, as well as for the Kardar-Parisi-Zhang equation. We locate and measure these currents and show that they manifest in real space as propagating modes localized in regions with nonvanishing gradients of the fields.

Tuning nonequilibrium phase transitions with inertia

In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation-dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. This density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions.

Pulsed Interaction Signals as a Route to Biological Pattern Formation

We identify a mechanism for biological spatial pattern formation arising when the signals that mediate interactions between individuals in a population have pulsed character. Our general population-signal framework shows that while for a slow signal-dynamics limit no pattern formation is observed for any values of the model parameters, for a fast limit, on the contrary, pattern formation can occur. Furthermore, at these limits, our framework reduces, respectively, to reaction-diffusion and spatially nonlocal models, thus bridging these approaches.

Active Refrigerators Powered by Inertia

We present the operational principle for a refrigerator that uses inertial effects in active Brownian particles to locally reduce their (kinetic) temperature by 2 orders of magnitude below the environmental temperature. This principle exploits the peculiar but so-far unknown shape of the phase diagram of inertial active Brownian particles to initiate motility-induced phase separation in the targeted cooling regime only. Remarkably, active refrigerators operate without requiring isolating walls opening the route toward using them to systematically absorb and trap, e.g., toxic substances from the environment.

Active nonreciprocal attraction between motile particles in an elastic medium

We show from experiments and simulations on vibration-activated granular matter that self-propelled polar rods in an elastic medium on a substrate turn and move towards each other. We account for this effective attraction through a coarse-grained theory of a motile particle as a moving point-force density that creates elastic strains in the medium that reorient other particles. Our measurements confirm qualitatively the predicted features of the distortions created by the rods, including the |x|^{-1/2} tail of the trailing displacement field and nonreciprocal sensing and pursuit. A discrepancy between the magnitudes of displacements along and transverse to the direction of motion remains. Our theory should be of relevance to the interaction of motile cells in the extracellular matrix or in a supported layer of gel or tissue.

Interaction from structure using machine learning: in and out of equilibrium

Prediction of pair potential given a typical configuration of an interacting classical system is a difficult inverse problem. There exists no exact result that can predict the potential given the structural information. We demonstrate that using machine learning (ML) one can get a quick but accurate answer to the question: "which pair potential lead to the given structure (represented by pair correlation function)?" We use artificial neural network (NN) to address this question and show that this ML technique is capable of providing very accurate prediction of pair potential irrespective of whether the system is in a crystalline, liquid or gas phase. We show that the trained network works well for sample system configurations taken from both equilibrium and out of equilibrium simulations (active matter systems) when the later is mapped to an effective equilibrium system with a modified potential. We show that the ML prediction about the effective interaction for the active system is not only useful to make prediction about the MIPS (motility induced phase separation) phase but also identifies the transition towards this state.