Work and reversibility in quantum thermodynamics

TL;DR

This paper investigates the relationship between irreversibility, entropy production, and work extraction in quantum thermodynamics, establishing a quantitative link between process reversibility and work gain using resource theory and quantum information tools.

Contribution

It introduces a framework connecting reversibility, entropy production, and work in quantum thermodynamics, utilizing the Petz recovery channel to quantify reversibility.

Findings

Entropy production depends on process reversibility.

Reversibility is linked to work extractable from quantum states.

Explicit reversal operation using Petz recovery channel is provided.

Abstract

It is a central question in quantum thermodynamics to determine how irreversible is a process that transforms an initial state $\rho$ to a final state $\sigma$, and whether such irreversibility can be thought of as a useful resource. For example, we might ask how much work can be obtained by thermalizing $\rho$ to a thermal state $\sigma$ at temperature $T$ of an ambient heat bath. Here, we show that, for different sets of resource-theoretic thermodynamic operations, the amount of entropy produced along a transition is characterized by how reversible the process is. More specifically, this entropy production depends on how well we can return the state $\sigma$ to its original form $\rho$ without investing any work. At the same time, the entropy production can be linked to the work that can be extracted along a given transition, and we explore the consequences that this fact has for our results. We also exhibit an explicit reversal operation in terms of the Petz recovery channel coming from quantum information theory. Our result establishes a quantitative link between the reversibility of thermodynamical processes and the corresponding work gain.