On the role of initial coherence in the spin phase-space entropy production rate

Recent studies have pointed out the intrinsic dependence of figures of merit of thermodynamic relevance—such as work, heat and entropy production—on the amount of quantum coherences that is made available to a system. However, whether coherences hinder or enhance the value taken by such quantifiers of thermodynamic performance is yet to be ascertained. We show that, when considering entropy production generated in a process taking a finite-size bipartite quantum system out of equilibrium through local non-unitary channels, no general monotonicity relationship exists between the entropy production and degree of quantum coherence in the state of the system. A direct correspondence between such quantities can be retrieved when considering specific forms of open-system dynamics applied to suitably chosen initial states. Our results call for a systematic study of the role of genuine quantum features in the non-equilibrium thermodynamics of quantum processes.
European Union (EU); Horizon 2020; Horizon Europe; FET-Open project TEQ; EIC Pathfinder project QuCoM; Leverhulme Trust Research Project Grant UltraQuTe; Scientific and Technological Research Council of Turkey (TÜBİTAK); BAGEP Award of the Science Academy; We acknowledge discussions with Matteo Brunelli in the early development of the problem. G Z and B Ç are grateful to Steve Campbell for hospitality within his group at University College Dublin during the final stages of this project. The Royal Society Wolfson Fellowship (RSWF/R3/183013), the UK EPSRC (Grant EP/T028424/1) and the Department for the Economy Northern Ireland under the US-Ireland R&D Partnership Programme.