Fundamental relation between entropy production and heat current

TL;DR

This paper establishes fundamental inequalities linking entropy production rate to the speed of energy exchange in classical Markov processes, highlighting that faster energy transfer causes higher entropy production, especially in linear response regimes.

Contribution

The paper derives two new inequalities connecting entropy production and energy exchange speed, applicable to general and local detailed-balance Markov processes, with demonstrated tightness in linear response.

Findings

Faster energy exchange induces larger entropy production.

Derived inequalities are tight in the linear response regime.

Applicable to both general and local detailed-balance Markov processes.

Abstract

We investigate the fundamental relation between entropy production rate and the speed of energy exchange between a system and baths in classical Markov processes. We establish the fact that quick energy exchange inevitably induces large entropy production in a quantitative form. More specifically, we prove two inequalities on instantaneous quantities: One is applicable to general Markov processes induced by heat baths, and the other is applicable only to systems with the local detailed-balance condition but is stronger than the former one. We demonstrate the physical meaning of our result by applying to some specific setups. In particular, we show that our inequalities are tight in the linear response regime.