Irreversible work and inner friction in quantum thermodynamic processes

TL;DR

This paper explores the concepts of irreversible work and inner friction in quantum thermodynamics, establishing their relationship with heat exchange, relative entropy, and fluctuation relations during non-equilibrium quantum processes.

Contribution

It introduces a unified framework for analyzing irreversible work and inner friction, linking them to heat exchange and relative entropy, and derives a fluctuation relation for inner friction.

Findings

Inner friction and irreversible work can be expressed as relative entropies.

A fluctuation relation for entropy production due to inner friction is established.

Inner friction can be characterized by its cumulants in quantum thermodynamic processes.

Abstract

We discuss the thermodynamics of closed quantum systems driven out of equilibrium by a change in a control parameter and undergoing a unitary process. We compare the work actually done on the system with the one that would be performed along ideal adiabatic and isothermal transformations. The comparison with the latter leads to the introduction of irreversible work, while that with the former leads to the introduction of inner friction. We show that these two quantities can be treated on equal footing, as both can be linked with the heat exchanged in thermalization processes and both can be expressed as relative entropies. Furthermore, we show that a specific fluctuation relation for the entropy production associated with the inner friction exists, which allows the inner friction to be written in terms of its cumulants.