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

TL;DR

This paper studies entropy production and time-reversal symmetry violations in models of polar active matter, revealing different nonequilibrium regimes and phase structures, including a novel crystal phase, through theoretical analysis and numerical simulations.

Contribution

It introduces a detailed analysis of entropy production scaling in active matter models, identifying regimes of equilibrium and nonequilibrium behavior, and explores the impact of variable choice and protocols on entropy production.

Findings

Divergent EPR indicates truly nonequilibrium dynamics at low noise.

Finite EPR with broken TRS occurs in marginally nonequilibrium regimes.

Numerical simulations confirm theoretical scaling relations and predictions.

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, 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.