Abstract
The irreversible work during a driving protocol constitutes one of the most widely studied measures in non-equilibrium 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 understand 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. For quenches in the transverse field, we find that for finite temperatures the contribution from coherence can, in certain cases, account for practically all of the entropy production. At low temperatures, however, the coherence presents a finite cusp at the critical point, whereas the entropy production diverges logarithmically. Alternatively, if the quench is performed in the anisotropy parameter, we find that there are situations where all of the entropy produced is due to quantum coherences.
Highlights
Driving a system out of equilibrium is always accompanied by a finite production of entropy
It has been shown that the irreversible work has an additional, genuinely quantum mechanical contribution, due to coherence produced by the driving protocol
We investigated the genuinely quantum-mechanical contribution of the generation of coherence to the production of entropy for quenches in the transverse field and in the anisotropy parameter of an XY model
Summary
Driving a system out of equilibrium is always accompanied by a finite production of entropy. The nonequilibrium nature of the process can be quantified by the irreversible work Wirr [Eq (2)] or, what is equivalent, the entropy production/nonequilibrium lag Sirr in Eq (3) This quantity, can be split as in Eq (4) into a contribution D [Eq (5)] related to changes in the population and a contribution C related to quantum coherence [Eq (6)]. It quantifies the difference between ρ and the dephased state τ [ρ ] This term measures the contribution to the nonequilibrium lag stemming solely from the quantum coherences generated by the driving protocol. Since both terms are individually nonnegative by construction, this shows how coherence increases the entropy produced in the process. While D(ρ ) diverges logarithmically at the critical point [82,104], C(ρ ) presents a cusp
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