Quantum coherence and criticality in irreversible work

Abstract

The irreversible work during a driving protocol constitutes one of the most widely studied measures in nonequilibrium thermodynamics, as it constitutes a proxy for entropy production. In quantum systems, it has been shown that the irreversible work has an additional, genuinely quantum mechanical contribution, due to coherence produced by the driving protocol. The goal of this paper is to explore this contribution in systems that undergo a quantum phase transition. Substantial effort has been dedicated in recent years to understanding the role of quantum criticality in work protocols. However, practically nothing is known about how coherence contributes to it. To shed light on this issue, we study the entropy production in infinitesimal quenches of the one-dimensional XY model. We find that coherence plays a significant role in the entropy production and can even account for most of it in certain situations. Moreover, at low temperatures, the coherence presents a finite cusp at the critical point, whereas the entropy production diverges logarithmically. For high temperatures, however, the coherence presents a kink at the critical point indicating the quantum phase transition that occurs only at T=0. Alternatively, if the quench is performed in the anisotropy parameter, then we find that there are situations where all of the entropy produced is due to quantum coherences.