Fluctuations of path-dependent thermodynamic quantities in open quantum systems via two-point system-only measurements

TL;DR

This paper introduces a system-only measurement approach to evaluate thermodynamic fluctuations in open quantum systems, deriving exact fluctuation equalities and correction factors applicable to various dynamics.

Contribution

It provides a novel, flexible framework for analyzing path-dependent thermodynamic quantities in open quantum systems, including strong coupling and non-Markovian effects.

Findings

Exact fluctuation equalities for work and heat in open quantum systems.

Pure decoherence dynamics do not contribute heat, preserving Jarzynski's equality.

Correction factors to Jarzynski's equality depend on the system's dynamical class.

Abstract

We propose a method to evaluate general thermodynamic fluctuations in open quantum systems, based on performing a two-point measurement scheme on the system using dynamics-dependent thermodynamic observables. Our approach allows one to obtain exact equalities for fluctuations of path-dependent thermodynamic quantities such as work and heat, and to isolate correction factors to Jarzynski's equality, requiring only access to the system degrees of freedom. This framework is flexible and can be applied to the limiting case of closed systems, recovering previous, yet seemingly contradictory, results from the literature. Moreover, the formalism admits a straightforward extension to strongly coupled open quantum systems. We investigate the effect of specific dynamical classes on the fluctuation relations, and show that the pure decoherence case is particularly special, as it deterministically does not contain any heat contribution and thus constitutes a class of open system dynamics for which the Jarzynski equality for work fluctuations is identically true at any coupling strength. Finally, we look explicitly at the shape and size of the correction factors to Jarzynski's equality for a qubit undergoing phase covariant dynamics, both in the weakly-coupled regime and in the deep non-Markovian regime.