A meaningful expansion around detailed balance

TL;DR

This paper develops a systematic expansion of the stationary distribution for Markovian open systems driven away from equilibrium, incorporating both entropy flux and dynamical activity to understand nonlinear responses.

Contribution

It generalizes the McLennan formula to higher orders, integrating dynamical activity with entropy flux for a comprehensive nonequilibrium analysis.

Findings

Expansion valid for exponential ergodicity cases

Higher-order terms include dynamical activity

Provides a framework for nonlinear response analysis

Abstract

We consider Markovian dynamics modeling open mesoscopic systems which are driven away from detailed balance by a nonconservative force. A systematic expansion is obtained of the stationary distribution around an equilibrium reference, in orders of the nonequilibrium forcing. The first order around equilibrium has been known since the work of McLennan (1959), and involves the transient irreversible entropy flux. The expansion generalizes the McLennan formula to higher orders, complementing the entropy flux with the dynamical activity. The latter is more kinetic than thermodynamic and is a possible realization of Landauer's insight (1975) that, for nonequilibrium, the relative occupation of states also depends on the noise along possible escape routes. In that way nonlinear response around equilibrium can be meaningfully discussed in terms of two main quantities only, the entropy flux and the dynamical activity. The expansion makes mathematical sense as shown in the simplest cases from exponential ergodicity.