Contributions from populations and coherences in non-equilibrium entropy production

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.

Thermodynamic length and work optimisation for Gaussian quantum states

“…More recently, developments in quantum thermodynamics [5] have led to a growing interest towards understanding how quantum mechanical effects impart signatures on the statistics of work [6][7][8], alongside the usual influence of classical stochastic fluctuations. A range of interrelated phenomena have been shown to affect the behaviour of work in the quantum regime, including quantum correlations [9], violations of macro-realism [10,11], contextuality [12], quantum coherence [13][14][15][16] and quantum measurement effects [17].…”

Quantum quench thermodynamics at high temperatures

“…The entropy production, however, can be consistently split into two parts, associated with classical and quantum contributions, the latter steaming from quantum coherences [23][24][25][26]. Beyond unitary work protocols [24], particularly in critical systems [26,27], this type of splittings has found many applications like in work extraction protocols [28], relaxation towards equilibrium [23,29], quasi-static evolution and consequences of coherences to the fluctuation-dissipation theorem [25,30], thermodynamics resource theory [31] and quantum optics thermodynamics [32]. In [26,27] we hinted at the fact that this contributions could individually signal the existence of a critical point at any temperature.…”

“…Beyond unitary work protocols [24], particularly in critical systems [26,27], this type of splittings has found many applications like in work extraction protocols [28], relaxation towards equilibrium [23,29], quasi-static evolution and consequences of coherences to the fluctuation-dissipation theorem [25,30], thermodynamics resource theory [31] and quantum optics thermodynamics [32]. In [26,27] we hinted at the fact that this contributions could individually signal the existence of a critical point at any temperature. The aim of this paper is to further explore and clarify this point.…”

“…Let us consider the quench δg = g τ − g 0 to be small. Then we can make a Taylor expansion, and the entropy production can be simplified to [25,26]…”

“…The term Λ qu quantifies the entropy production associated with the coherences generated by a noncommuting drive. This expansion works in the range of parameters such that β|δg| 1 [26]. And both contributions in Eq.…”