Equilibrium, fluctuation relations and transport for irreversible deterministic dynamics

TL;DR

This paper demonstrates that fluctuation relations and equilibrium properties can hold in irreversible deterministic systems, showing that microscopic irreversibility does not affect macroscopic transport and response behaviors.

Contribution

It provides analytical and numerical evidence that fluctuation relations extend to irreversible systems and shows that transport coefficients and equilibrium-like detailed balance persist despite microscopic irreversibility.

Findings

Fluctuation relation for phase space contraction rate applies to irreversible systems.

Transport coefficients are unaffected by microscopic irreversibility.

A form of detailed balance holds in relevant variables despite irreversibility.

Abstract

In a recent paper [M. Colangeli \textit{et al.}, J.\ Stat.\ Mech.\ P04021, (2011)] it was argued that the Fluctuation Relation for the phase space contraction rate $\Lambda$ could suitably be extended to non-reversible dissipative systems. We strengthen here those arguments, providing analytical and numerical evidence based on the properties of a simple irreversible nonequilibrium baker model. We also consider the problem of response, showing that the transport coefficients are not affected by the irreversibility of the microscopic dynamics. In addition, we prove that a form of \textit{detailed balance}, hence of equilibrium, holds in the space of relevant variables, despite the irreversibility of the phase space dynamics. This corroborates the idea that the same stochastic description, which arises from a projection onto a subspace of relevant coordinates, is compatible with quite different underlying deterministic dynamics. In other words, the details of the microscopic dynamics are largely irrelevant, for what concerns properties such as those concerning the Fluctuation Relations, the equilibrium behaviour and the response to perturbations.