Work and reversibility in quantum thermodynamics

Stephanie Wehner, Mark M. Wilde, Mischa P. Woods

Published 2015-06-26Version 1

It is a central question in quantum thermodynamics to determine how much work can be gained by a process that transforms an initial state $\rho$ to a final state $\sigma$. 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 large systems, or when allowing slightly inexact catalysis, the amount of work is characterized by how reversible the process is. More specifically, the amount of work to be gained depends on how well we can return the state $\sigma$ to its original form $\rho$ without investing any work. We proceed to 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.