Entropic fluctuations of quantum dynamical semigroups

TL;DR

This paper establishes a general entropic fluctuation theorem for finite-dimensional quantum dynamical semigroups with detailed balance, linking entropy transport fluctuations to spectral properties and deriving classical response relations.

Contribution

It introduces a fluctuation theorem for quantum dynamical semigroups satisfying detailed balance, connecting cumulant generating functions to spectral deformations and symmetries.

Findings

Proves a fluctuation theorem relating entropy transport to generator spectrum.

Shows cumulant generating function satisfies Evans-Searles and translation symmetries.

Derives Kubo's and Onsager's relations from symmetries near equilibrium.

Abstract

We study a class of finite dimensional quantum dynamical semigroups exp(tL) whose generators L are sums of Lindbladians satisfying the detailed balance condition. Such semigroup arise in the weak coupling (van Hove) limit of Hamiltonian dynamical systems describing open quantum systems out of equilibrium. We prove a general entropic fluctuation theorem for this class of semigroups by relating the cumulant generating function of entropy transport to the spectrum of a family of deformations of the generator L. We show that, besides the celebrated Evans-Searles symmetry, this cumulant generating function also satisfies the translation symmetry recently discovered by Andrieux et al., and that in the linear regime near equilibrium these two symmetries yield Kubo's and Onsager's linear response relations.