Analysis of entropy production in finitely slow processes between nonequilibrium steady states

TL;DR

This paper studies entropy production during finite-time transitions between nonequilibrium steady states in Markov processes, using an improved adiabatic approximation to include nonadiabatic corrections and analyze thermodynamic metrics.

Contribution

It introduces a systematic method to compute nonadiabatic corrections to entropy production in slow processes, extending previous adiabatic approximations.

Findings

Leading adiabatic contribution matches known results

Nonadiabatic corrections are expressed via thermodynamic metrics

Numerical analysis confirms theoretical predictions in a two-state system

Abstract

We investigate entropy production in finitely slow transitions between nonequilibrium steady states in Markov jump processes using the improved adiabatic approximation method proposed by Takahashi, Fujii, Hino and Hayakawa [1]. This method provides systematic improvement of the adiabatic approximation on infinitely slow transitions from which we obtain nonadiabatic corrections and has a close relationship with the slow driving perturbation [2, 3]. We analyze two types of excess entropy production of Sagawa and Hayakawa [4] and Hatano and Sasa [5] as examples, and confirm that the leading adiabatic contribution reproduces the known results, and then obtain nonadiabatic corrections written in terms of thermodynamic metrics defined in protocol parameter spaces. We also numerically study the resulting excess entropy production in a two-state system.