Clausius Inequality for Finite Baths Reveals Universal Efficiency Improvements

TL;DR

This paper revises the second law for finite heat baths using Clausius' inequality, revealing that nanoscale heat engines can operate more efficiently than previously estimated, with implications for quantum thermodynamics.

Contribution

It introduces a rigorous formulation of the second law for finite baths based on Clausius' inequality, extending Landauer's principle and efficiency bounds for nanoscale heat engines.

Findings

Finite baths lead to less irreversible processes.

Heat engine efficiency is higher with finite baths.

The approach is accessible via average bath energy.

Abstract

We study entropy production in nanoscale devices, which are coupled to finite heat baths. This situation is of growing experimental relevance, but most theoretical approaches rely on a formulation of the second law valid only for infinite baths. We fix this problem by pointing out that already Clausius' paper from 1865 contains an adequate formulation of the second law for finite heat baths, which can be also rigorously derived from a microscopic quantum description. This Clausius' inequality shows that nonequilibrium processes are less irreversible than previously thought. We use it to correctly extend Landauer's principle to finite baths and we demonstrate that any heat engine in contact with finite baths has a higher efficiency than previously thought. Importantly, our results are easy to study, requiring only the knowledge of the average bath energy.