Nonequilibrium Response for Markov Jump Processes: Exact Results and Tight Bounds

TL;DR

This paper develops an algebraic framework to analyze the response of nonequilibrium Markov jump processes, providing explicit formulas and bounds for how steady states react to various perturbations, advancing understanding in nonequilibrium statistical physics.

Contribution

It introduces a new algebraic method to derive explicit response expressions and bounds for Markov jump processes under arbitrary perturbations, generalizing previous approaches.

Findings

Explicit response formulas for edge currents and traffic.

Simple bounds on responses to perturbations.

Recovery of known results using a new algebraic approach.

Abstract

Generalizing response theory of open systems far from equilibrium is a central quest of nonequilibrium statistical physics. Using stochastic thermodynamics, we develop an algebraic method to study the response of nonequilibrium steady state to arbitrary perturbations. This allows us to derive explicit expressions for the response of edge currents as well as traffic to perturbations in kinetic barriers and driving forces. We also show that these responses satisfy very simple bounds. For the response to energy perturbations, we straightforwardly recover results obtained using nontrivial graph-theoretical methods.