arXiv subjects

Michael E. Cates

Publications and source records attributed to Michael E. Cates.

At least 19 recordsLinked to original sources

arXiv2026

Microscopic Dynamical Entropy I: Quantifying Hamiltonian Irreversibility in Large and Small Systems

We introduce a Microscopic Dynamical Entropy (MDE) for Hamiltonian systems, defined with respect to a chosen partition of degrees of freedom into a system X and its environment Y. The construction is based on the conditional phase-space volume (CPV), or conditional Boltzmann entropy, associated with the unmonitored degrees of freedom Y. The MDE is a microscopically defined entropy functional of the marginal distribution $\rho_X(t)$, obtained by discarding conditional microscopic information associated with Y from the Gibbs entropy of the joint XY system, while retaining exact Hamiltonian dynamics. This construction clarifies the microscopic origin of thermal entropy. The dependence of MDE solely on $\rho_X(t)$ is consistent with the thermodynamic assumption that the entropy increment of a heat bath Y depends on its heat content and temperature, not on details of its probability distribution. Indeed, the MDE recovers dS = dQ/T connecting entropy increments to heat flow between system and environment. More generally, it provides a consistent description of irreversible relaxation under exact Hamiltonian dynamics, while permitting transient entropy decreases in small systems and in spin-echo type protocols. Under time-scale separation between X and Y, the MDE becomes strictly monotonic in time, recovering the familiar structure of irreversible thermodynamics. The MDE can foreshadow thermodynamics even in a small isolated Hamiltonian system, if X is a well chosen subset of its degrees of freedom. An example is the centre of mass of interacting particles confined to a box. Even for as few as N=10 particles, the MDE increases during relaxation towards a maximum at equilibrium, with increasing monotonicity at larger N. Taken together, our results show that the MDE offers a microscopic interpretation of nonequilibrium thermal entropy and its time dependence within exact Hamiltonian dynamics.

cond-mat.stat-mech↗

arXiv2026

Microscopic Dynamical Entropy II: Statistical and Stochastic Thermodynamics of Hamiltonian Systems

The Microscopic Dynamical Entropy (MDE) introduced in Ref. [1] describes irreversible relaxation of selected variables x within a finite closed Hamiltonian system of fixed total energy E. Here we extend the framework to arbitrary total-energy distributions and time-dependent Hamiltonians. This allows work interactions with external agents or protocols, crucial in stochastic and classical thermodynamics, and driven systems more generally, to be addressed directly. The central step is to reduce the full microscopic description in terms of selected variables x and unmonitored variables y to one in terms of the selected variables and the instantaneous total energy (x,E). The unmonitored degrees of freedom y in Y enter through their conditional phase-space volume (CPV) $\Omega_Y(x,E,t)$. This construction allows work and heat to be defined directly for finite Hamiltonian composites, including cases where Y is so small that its temperature is not well defined. We demonstrate monotonic MDE growth, corresponding to the macroscopic second law, under mixing and time-scale separation even for driven systems with arbitrary energy distributions. At trajectory level, we derive detailed and integral fluctuation relations for the MDE, generalising standard large-bath results. We verify these numerically in a driven few-particle Hamiltonian system, showing the emergence of stochastic thermodynamics for collective coordinates, such as the centre-of-mass position, even in closed systems with only ten or twenty degrees of freedom. Physically, these fluctuation relations connect irreversibility to the change in the number of unmonitored microstates compatible with initial and final data for the observed coordinates. Together, our results provide a finite-system Hamiltonian foundation for the emergence of classical and stochastic thermodynamics and extend their applicability to surprisingly small heat baths.

cond-mat.stat-mech↗

arXiv2026

Nucleation and time-reversal symmetry breaking in nonconserved scalar field theories

Classical nucleation theory (CNT) describes the formation of a stable phase from a metastable one in terms of a single reaction coordinate that corresponds to the radius of a nucleating droplet. In this work, we provide a full account of nonequilibrium nucleation theory (NNT), which generalizes CNT to non-equilibrium field theories with non-conserved order parameter. We present two equivalent derivations of the dynamics of the droplet radius: a stochastic route, based on a direct projection of the stochastic field equation onto the radial reaction coordinate, and a route based on the minimization of the Freidlin-Wentzell action. Crucially, the quasipotential barrier predicted by NNT differs from the one found when assuming the instanton to be the time-reversal of the relaxation dynamics. Whereas the interfacial density profile differs from that on the relaxation path, an analytical derivation of NNT remains possible using a careful definition of the reaction coordinate. This leverages the perturbative structure that (in common with CNT) emerges in the limit of large critical radius. We further derive with similar techniques the dynamics of capillary waves, whose stability is required for the CNT/NNT precept of a near-spherical droplet to prevail. After deriving our theory for generic non-conserved field-theories, we address two explicit examples: a non-equilibrium generalization of Model A (Active Model A), and a population dynamics model (with two choices of noise that each break time-reversal symmetry). In both cases, we validate our analytical NNT against numerical results obtained by action minimization, with excellent agreement. NNT provide a systematic framework for constructing nucleation theories in a broad class of non-equilibrium systems from active matter, reaction-diffusion systems and population dynamics.

cond-mat.stat-mech↗

arXiv2026

Non-equilibrium coupling to a diffusing density breaks Ising universality

The Ising universality class is remarkably robust to non-equilibrium perturbations, which generically flow to zero under renormalization. We show that this robustness fails when an order parameter is coupled nonreciprocally to a conserved diffusive density. Below $d_c=4$, the renormalization group flows to a fast-diffusion fixed point at which the density acts as a long-range multiplicative noise, producing a novel universality class. The non-equilibrium nature of the fixed point is manifest in the large-scale violation of the fluctuation-dissipation relations, reflected in a splitting of the scaling exponents of the two-point correlation and response functions--a measurable hallmark of non-equilibrium critical fluctuations. A two-loop calculation establishes the stability of this fixed point but yields a small correction-to-scaling exponent $\omega\approx0.020$ in $d=3$, implying strong finite-size corrections. An all-orders modified Harris criterion $\nu>2/(d+z-2)$ confirms that the BIM fixed point governs criticality in $d=3$, with Ising universality recovered only at $d=2$.

cond-mat.stat-mech↗

arXiv2026

Nonequilibrium nucleation theory for nonconserved fields: from active matter to population dynamics

Classical nucleation theory (CNT) describes the formation of a stable phase from a metastable one. In equilibrium systems, it quantifies the free-energy competition between a favorable bulk gain and an unfavorable interfacial cost. For systems without detailed balance, the corresponding nonequilibrium nucleation theory (NNT) was so far developed only for cases with a conserved order parameter, such as active fluid-fluid phase separation. Here we construct the NNT for systems with a (single, scalar) nonconserved order parameter. Unlike in the conserved case, the nucleation barrier controlling (noise-driven) droplet growth is profoundly altered by deviations in the interfacial density profile from the one arising during (deterministic) droplet relaxation. The barrier can nonetheless be analysed by carefully defining the reaction coordinate (droplet radius) to project out those deviations. We give explicit NNT predictions for models drawn from population dynamics and active matter, finding excellent agreement with numerical studies.

cond-mat.stat-mech↗

arXiv2026

Generic nonlocal statistics of the stationary measure in conserved active systems

The stationary measure of equilibrium systems with detailed balance follows a Boltzmann distribution, so that for short-ranged interactions the measure is local, meaning that distant spatial domains are statistically independent. In contrast, active systems break detailed balance, and can have nonlocal stationary measure even for fully local dynamics. Here, by expanding in nonlinearity about a Gaussian-model limit, we construct the measure perturbatively deep in the disordered phase for a class of models that includes Active Model A, Active Model B+, Model AB, the Nonreciprocal Cahn--Hilliard model, and the Toner--Tu model. In this regime, nonlocality is linked to a dynamical conservation law. Our results generically preclude construction of a Landau--Ginzburg expansion of the stationary measure (as opposed to the dynamical equations) for conserved active field theories.

cond-mat.stat-mech↗

arXiv2026

Coupling between Phase Separation and Geometry on a Closed Elastic Curve: Free Energy Minimization and Dynamics

We study the free energy and dynamics of a closed elastic filament (a one-dimensional curve in two dimensions) coupled to a scalar concentration field representing, for example, an absorbed species. The density variable has a tendency to phase-separate whereas the local spontaneous curvature is concentration-dependent. We address analytically and by simulation both the free energy landscape and the dynamics (the latter comprising a coupled Willmore flow and Cahn--Hilliard gradient flow on the full differential geometry of a closed filament), addressing issues that previous work typically sidestepped by restricting to the Monge gauge. Specifically we find that the closure constraint for a deformable filament qualitatively changes the free energy landscape compared with either a rigid closed filament or an open elastic one, admitting metastable and stable states with more than one domain of each type. By numerical global free energy minimization we explore equilibrium morphologies across a wide range of model parameters. For selected parameter values we present fully dynamical results, tracking the time evolution of the various contributions to the free energy and confirming the emergence of both metastable and equilibrium multi-domain morphologies.

cond-mat.soft↗

arXiv2026

Active Cahn-Hilliard theory for nonequilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation

Phase-separating active systems can display phenomenology that is impossible in equilibrium. The binodal densities are not solely determined by a bulk (effective) free energy, but also affected by gradient terms, while capillary waves and Ostwald processes are determined by three distinct interfacial tensions. These and related phenomena were so far explained at continuum level using a top-down minimal theory (Active Model B+). This theory, by Taylor-expanding in the scalar order parameter (or density), effectively assumes that phase separation is weak, which is not true across most of the phase diagram. Here, we develop a quantitative account of active phase separation, by introducing an active counterpart of Cahn-Hilliard theory, constructing the density current from all possible terms with up to four spatial derivatives without Taylor-expanding in the density. From this O(grad^4) theory, we show how to compute binodals and interfacial tensions for arbitrary choices of the five density-dependent 'coefficient functions' that specify the theory (replacing the four constant coefficients of Active Model B+). We further consider a particle model composed of thermal quorum-sensing active particles (tQSAPs) yielding a fully specified example of the O(grad^4) theory upon coarse-graining. We find that to coarse-grain consistently at O(grad^4) requires a systematic procedure, based on multiple-scale analysis, to eliminate fast-evolving orientational moments. Using this, we calculate from microscopic physics all five coefficient functions of the active Cahn-Hilliard theory for tQSAPs. We identify contributions that were missed in previous continuum theories, and show how neglecting them becomes justified only in the limit of large quorum-sensing range parameter. Comparison with particle simulations of tQSAPs shows that our O(grad^4) theory improves on previous continuum models [...]

cond-mat.stat-mech↗

arXiv2025

Non-equilibrium pathways between cluster morphologies in active phase separation: necking, rupture and cavitation

We investigate the dynamical pathways of a morphological transition in a two-dimensional active lattice gas undergoing motility-induced phase separation. The transition is between two locally stable morphologies of the liquid cluster: a system-spanning "slab" and a compact "droplet". We generate trajectories of this transition in both directions using forward flux sampling. We find that the droplet-to-slab transition always follows a similar mechanism to its equilibrium counterpart, but the reverse (slab-to-droplet) transition depends on rare non-equilibrium fluctuations. At low P\'eclet numbers the equilibrium and non-equilibrium pathways compete, while at high P\'eclet numbers the equilibrium pathway is entirely suppressed, and the only allowed mechanism involves a large vapour bubble. We discuss the implications of these findings for active matter systems more generally.

cond-mat.soft↗

arXiv2025

Nonreciprocal dynamics with weak noise: aperiodic "Escher cycles" and their quasipotential landscape

We present an explicit construction of the Freidlin-Wentzell quasipotential of a stochastic system with two degrees of freedom and nonreciprocal interactions. This model undergoes noise-induced transitions between four metastable attractors, forming recurrent but aperiodic ``Escher cycles,'' similar to the cyclic nucleation dynamics observed in the nonreciprocal Ising model. We calculate the quasipotential analytically to first order in nonreciprocality. We characterise it along a one-dimensional reaction coordinate that connects the attractors, and we also obtain the full two-dimensional landscape, at leading order in perturbation theory. The resulting landscapes feature flat regions and extended plateaus, together with non-differentiable switching lines. These singular structures arise from two geometric mechanisms: the handover of dominance between competing transition paths, and the competition between basins of attraction. The system provides a rare case where the geometry of nonequilibrium rare events can be fully resolved, and a simple analytically tractable example of a quasipotential in more than one coordinate that captures a rich set of nonequilibrium features.

cond-mat.stat-mech↗

arXiv2025

Spontaneous Ratchet Currents and Transition Dynamics in Active Wetting

Self-propelled particles accumulate on repulsive barriers in so-called active wetting, whose relationship with equilibrium wetting remains unclear. Using an exact (noiseless) hydrodynamic framework for an active lattice gas, we show, using a slit geometry with periodic boundary conditions, that active matter exhibits both fully-wet and partially-wet states, with a critical wetting transition between them. Furthermore, we demonstrate the existence of a spontaneous-symmetry-breaking ratchet current in the partially-wet state, leading to departure of the bulk densities from their binodal values and the emergence of a novel dynamical pathway for the full-to-partial wetting transition. We elucidate this modified dynamical pathway using a minimal model. The results, while establishing a direct connection between active and equilibrium wetting, also identify the nonequilibrium consequences of activity.

cond-mat.stat-mech↗

arXiv2025

What exactly is 'active matter'?

As the study of active matter has developed into one of the most rapidly growing subfields of condensed matter physics, more and more kinds of physical systems have been included in this framework. While the word 'active' is often thought of as referring to self-propelled particles, it is also applied to a large variety of other systems such as non-polar active nematics or certain particles with non-reciprocal interactions. Developing novel forms of active matter, as attempted, e.g., in the framework of quantum active matter, requires a clear idea of what active matter is. Here, we critically discuss how the understanding of active matter has changed over time, what precisely a definition of 'active matter' can look like, and to what extent it is (still) possible to define active matter in a way that covers all systems that are commonly understood as active matter while distinguishing them from other driven systems. Moreover, we discuss the definition of an 'active field theory', where 'active' is used as an attribute of a theoretical model rather than of a physical system. We show that the usage of the term 'active' requires agreement on a coarse-grained viewpoint. We discuss the meaning of 'active' both in general terms and via the specific examples of chemically driven particles, ultrasound-driven particles, active nematics, particles with non-reciprocal interactions, intracellular phase separation, and quantum active matter.

cond-mat.soft↗

arXiv2025

Hyperuniformity at the Absorbing State Transition: Perturbative RG for Random Organization

Hyperuniformity, where the static structure factor obeys $S(q)\sim q^{\varsigma}$ with $\varsigma> 0$, emerges at criticality in systems having multiple, symmetry-unrelated, absorbing states. Important examples arise in periodically sheared suspensions and amorphous solids; these lie in the random organisation (RO) universality class, for which analytic results for $\varsigma$ are lacking. Here, using Doi-Peliti field theory and perturbative RG about a Gaussian model, we find $\varsigma = 0^+$ and $\varsigma= 2\epsilon/9 + O(\epsilon^2)$ in dimension $d>d_c=4$ and $d=4-\epsilon$ respectively. Our calculations assume that renormalizability is sustained via a certain pattern of cancellation of strongly divergent terms. These cancellations allow the upper critical dimension to remain $d_c = 4$, as is known for RO, while generic perturbations (e.g., those violating particle conservation) would typically flow to a fixed point with $d_c=6$. The assumed cancellation pattern is closely reminiscent of a long-established one near the tricritical Ising fixed point. (This has $d_c=3$, although generic perturbations flow towards the Wilson-Fisher fixed point with $d_c = 4$.) We show how hyperuniformity in RO emerges from anticorrelation of strongly fluctuating active and passive densities. Our calculations also yield the remaining exponents to order $\epsilon$, surprisingly without recourse to functional RG. These exponents coincide as expected with the Conserved Directed Percolation (C-DP) class which also contains the Manna Model and the quenched Edwards-Wilkinson (q-EW) model. Importantly however, our $\varsigma$ differs from one found via a mapping to q-EW. That mapping neglects a conserved noise in the RO action, which we argue to be dangerously irrelevant. Thus, although other exponents are common to both, the RO and C-DP universality classes have different exponents for hyperuniformity.

cond-mat.stat-mech↗

arXiv2025

Wetting and Pattern Formation in Non-Reciprocal Ternary Phase Separation

Non-reciprocal interactions are among the simplest mechanisms that drive a physical system out of thermal equilibrium, leading to novel phenomena such as oscillatory pattern formation. In this paper, we introduce a ternary phase separation model, with non-reciprocal interactions between two of the three phases and a spectator phase that mimics a boundary. Through numerical simulations, we uncover three distinct phase behaviours: a quasi-static regime, characterized by well-defined non-equilibrium contact angles at the three phase contact line; a limit cycle regime, with the three bulk phases rotating around the three phase contact line; and a travelling wave regime, featuring persistent directional motion. We complement our numerical findings with analytical examination of linear stability and the wave propagation speed near equilibrium. Our model provides a minimal framework for extending classical equilibrium wetting theory to active and non-equilibrium systems.

cond-mat.soft↗

arXiv2025

Hydrodynamic theory of wetting by active particles

The accumulation of self-propelled particles on repulsive barriers is a widely observed feature in active matter. Despite being implicated in a broad range of biological processes, from biofilm formation to cytoskeletal movement, wetting of surfaces by active particles remains poorly understood. In this work, we study this active wetting by considering a model comprising an active lattice gas, interacting with a permeable barrier under periodic boundary conditions, for which an exact hydrodynamic description is possible. We consider a hydrodynamic scaling limit that eliminates dynamical noise while retaining microscopic interpretability, enabling a precise characterisation of steady-states and their transitions. We demonstrate that the accumulation of active particles has remarkable similarities to equilibrium wetting, and that active wetting transitions display all the salient characteristics of the equilibrium critical wetting transition -- despite fundamental differences in underlying microscopic dynamics. However, our framework also enables the investigation of subtle but important nonequilibrium effects in active wetting, including a spontaneous ratchet effect which leads to a global steady-state current, departure of the bulk densities from their binodal values, and a novel dynamical transition pathway. Our results provide an intrinsically nonequilibrium framework in which to study active wetting, precisely demonstrating the connection to passive wetting while clarifying the nonequilibrium consequences of activity.

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

Hamiltonian Heat Baths, Coarse-Graining and Irreversibility: A Microscopic Dynamical Entropy from Classical Mechanics

The Hamiltonian evolution of an isolated classical system is reversible, yet the second law of thermodynamics states that its entropy can only increase. This has confounded attempts to identify a `Microscopic Dynamical Entropy' (MDE), by which we mean an entropy computable from the system's evolving phase-space density $\rho(t)$, that equates {\em quantitatively} to its thermodynamic entropy $S^{\rm th}(t)$, both within and beyond equilibrium. Specifically, under Hamiltonian dynamics the Gibbs entropy of $\rho$ is conserved in time; those of coarse-grained approximants to $\rho$ show a second law but remain quantitatively unrelated to heat flow. Moreover coarse-graining generally destroys the Hamiltonian evolution, giving paradoxical predictions when $\rho(t)$ exactly rewinds, as it does after velocity-reversal. Here we derive the MDE for an isolated system XY in which subsystem Y acts as a heat bath for subsystem X. We allow $\rho_{XY}(t)$ to evolve without coarse-graining, but compute its entropy by disregarding the detailed structure of $\rho_{Y|X}$. The Gibbs entropy of the resulting phase-space density $\tilde\rho_{XY}(t)$ comprises the MDE for the purposes of both classical and stochastic thermodynamics. The MDE obeys the second law whenever $\rho_X$ evolves independently of the details of Y, yet correctly rewinds after velocity-reversal of the full XY system.

cond-mat.stat-mech↗

arXiv2025

Active particles in moving traps: minimum work protocols and information efficiency of work extraction

We revisit the elementary problem of moving a particle in a harmonic trap in finite time with minimal work cost, and extend it to the case of an active particle. By comparing the Gaussian case of an Active Ornstein-Uhlenbeck particle and the non-Gaussian run-and-tumble particle, we establish general principles for thermodynamically optimal control of active matter beyond specific models. We show that the open-loop optimal protocols, which do not incorporate system-state information, are identical to those of passive particles but result in larger work fluctuations due to activity. In contrast, closed-loop (or feedback) control with a single (initial) measurement changes the optimal protocol and reduces the average work relative to the open-loop control for small enough measurement errors. Minimum work is achieved by particles with finite persistence time. As an application, we propose an active information engine which extracts work from self-propulsion. This periodic engine achieves higher information efficiency with run-and-tumble particles than with active Ornstein-Uhlenbeck particles. Complementing a companion paper that gives only the main results [arXiv:2407.18542], here we provide a full account of our theoretical calculations and simulation results. We include derivations of optimal protocols, work variance, impact of measurement uncertainty, and information-acquisition costs.

cond-mat.stat-mech↗