Quantum work statistics close to equilibrium

Abstract

We study the statistics of work, dissipation, and entropy production of a quantum quasi-isothermal process, where the system remains close to thermal equilibrium along the transformation. We derive a general analytic expression for the work distribution and the cumulant generating function. All work cumulants split into classical (noncoherent) and quantum (coherent) terms, implying that close to equilibrium there are two independent channels of dissipation at all levels of the statistics. For noncoherent or commuting protocols, only the first two cumulants survive, leading to a Gaussian distribution with its first two moments related through the classical fluctuation-dissipation relation. On the other hand, quantum coherence leads to positive skewness and excess kurtosis in the distribution, and we demonstrate that these non-Gaussian effects are a manifestation of asymmetry in relation to the resource theory of thermodynamics. Furthermore, we also show that the noncoherent and coherent contributions to dissipation satisfy independently the Evans-Searles fluctuation theorem, which sets strong bounds on the fluctuations in dissipation, with negative values exponentially suppressed. Our findings are illustrated in a driven two-level system and an Ising chain, where quantum signatures of the work distribution in the macroscopic limit are discussed.