Irreversibility in dynamical phases and transitions

TL;DR

This paper introduces a new measure called the entropy production factor (EPF) to quantify irreversibility in non-equilibrium dynamical systems, demonstrating its application in characterizing phase transitions in biochemical oscillations.

Contribution

The paper presents the EPF as a novel metric for analyzing irreversibility and applies it to study phase transitions in the Brusselator model.

Findings

EPF quantifies irreversibility distribution across frequencies.

EPF bounds the energetic cost of biochemical oscillations.

EPF characterizes the transition from local to global oscillations.

Abstract

Living and non-living active matter consumes energy at the microscopic scale to drive emergent, macroscopic behavior including traveling waves and coherent oscillations. Recent work has characterized non-equilibrium systems by their total energy dissipation, but little has been said about how dissipation manifests in distinct spatiotemporal patterns. We introduce a novel measure of irreversibility we term the entropy production factor (EPF) to quantify how time reversal symmetry is broken in field theories across scales. We use the EPF to characterize a dynamical phase transition in simulations of the Brusselator, a prototypical biochemically motivated non-linear oscillator. The EPF quantifies the distribution of irreversibility across spatiotemporal frequencies as the Brusselator transitions from local to global coherent oscillations, bounding the energetic cost to establish spatially synchronized biochemical oscillations.