Thermodynamic formalism and linear response theory for non-equilibrium steady states

TL;DR

This paper develops a thermodynamic formalism and linear response theory for non-equilibrium steady states, providing explicit formulas and insights into transport coefficients and conjugate quantities in driven systems.

Contribution

It introduces a general response formula for non-equilibrium steady states and explicitly constructs conjugate quantities for Markov processes, linking them to thermodynamic potentials.

Findings

Derived a simple, general response formula for non-equilibrium steady states.

Explicit construction of conjugate quantities for Markov processes.

Discussed formal analogy with thermodynamic potentials and implications.

Abstract

The accurate determination of transport coefficients in numerical simulations is becoming increasingly important in a wide range of applications. Here we consider the linear response in systems driven away from thermal equilibrium into a non-equilibrium steady state with non-vanishing entropy production rate. A simple derivation of a general response formula is presented. For Markov processes we explicitly construct the conjugate quantities and discuss their relation with known response formulas. Emphasis is put on the formal analogy with thermodynamic potentials and some consequences are discussed.