Role of Quantum Coherence in Thermodynamics

TL;DR

This paper establishes conditions for quantum system inter-convertibility under time-translation covariant evolution and explores the implications for quantum thermodynamics, particularly the resource theory of athermality and coherence.

Contribution

It provides necessary and sufficient conditions for quantum state inter-convertibility and clarifies the role of coherence in the reversibility of thermodynamic resource theories.

Findings

Resource theory of athermality is not reversible with sublinear coherence.

Considering sublinear free energy makes the pure-state athermality theory reversible.

The mixed-state case reversibility remains unproven.

Abstract

We find necessary and sufficient conditions to determine the inter-convertibility of quantum systems under time-translation covariant evolution, and use it to solve several problems in quantum thermodynamics both in the single-shot and asymptotic regimes. It is well known that the resource theory of quantum athermality is not reversible, but in PRL 111, 250404 (2013) it was claimed that the theory becomes reversible ``provided a sublinear amount of coherent superposition over energy levels is available". Here we show that if a sublinear amount of coherence among energy levels were considered free, then the resource theory of athermality would become trivial. Instead, we show that by considering a sublinear amount of energy to be free, the theory of athermality becomes reversible for the pure-state case. A proof of the same claim for the mixed-state case is still lacking.