Contributions from populations and coherences in non-equilibrium entropy production

TL;DR

This paper critiques the standard decomposition of non-equilibrium entropy production into population and coherence parts in quantum systems, proposing a new approach based on a dephased Hamiltonian and comparing it with existing methods.

Contribution

The authors introduce a novel decomposition of quantum entropy production that addresses shortcomings of the relative entropy of coherence approach, especially at low temperatures.

Findings

The new decomposition remains well-behaved at low temperatures.

It provides a clearer physical interpretation of coherence contributions.

Comparison with existing methods shows improved consistency in certain regimes.

Abstract

The entropy produced when a quantum system is driven away from equilibrium can be decomposed in two parts, one related with populations and the other with quantum coherences. The latter is usually based on the so-called relative entropy of coherence, a widely used quantifier in quantum resource theories. In this paper we argue that, despite satisfying fluctuation theorems and having a clear resource-theoretic interpretation, this splitting has shortcomings. First, it predicts that at low temperatures the entropy production will always be dominated by the classical term, irrespective of the quantum nature of the process. Second, for infinitesimal quenches, the radius of convergence diverges exponentially as the temperature decreases, rendering the functions non-analytic. Motivated by this, we provide here a complementary approach, where the entropy production is split in a way such that the contributions from populations and coherences are written in terms of a thermal state of a specially dephased Hamiltonian. The physical interpretation of our proposal is discussed in detail. We also contrast the two approaches by studying work protocols in a transverse field Ising chain, and a macrospin of varying dimension.