Quantum work statistics close to equilibrium

TL;DR

This paper analyzes quantum work statistics near equilibrium, revealing how quantum coherence influences the distribution's shape and dissipation channels, with implications for thermodynamic resource theories.

Contribution

It derives a general analytic expression for work distribution near equilibrium, distinguishing classical and quantum contributions, and explores their effects on fluctuation relations.

Findings

Work cumulants split into classical and quantum parts.

Quantum coherence causes non-Gaussian features like skewness.

Both contributions independently satisfy fluctuation theorems.

Abstract

We study the statistics of work, dissipation, and entropy production of a quantum quasi-isothermal process, where the system remains close to the 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 a classical (non-coherent) and quantum (coherent) term, implying that close to equilibrium there are two independent channels of dissipation at all levels of the statistics. For non-coherent 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 non-coherent and coherent contributions satisfy independently the Evans-Searles fluctuation theorem, which sets strong bounds on the statistics, with negative values of the dissipation being 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.