Generalized Clausius relation and power dissipation in non equilibrium stochastic systems

TL;DR

This paper generalizes thermodynamic concepts to Markov systems, establishing a Clausius equality, linking zero dissipation to detailed balance and zero power, and deriving power-dissipation inequalities near equilibrium.

Contribution

It extends thermodynamics to Markov systems, generalizes the Clausius inequality to an equality, and connects dissipation, detailed balance, and power production.

Findings

Clausius inequality becomes an equality in this framework

Zero dissipation implies detailed balance and zero power

Maximum power near equilibrium requires dissipation of the same order

Abstract

We extend certain basic and general concepts of thermodynamics to discrete Markov systems exchanging work and heat with reservoirs. In this framework we show that the celebrated Clausius inequality can be generalized and becomes an equality, significantly extending several recent results. We further show that achieving zero dissipation in a system implies that detailed balance obtains, and as a consequence there is zero power production. We obtain inequalities for power production under more general circumstances and show that near equilibrium obtaining maximum power production requires dissipation to be of the same order of magnitude.