Fluctuation-dissipation relations for thermodynamic distillation processes

TL;DR

This paper derives a fluctuation-dissipation relation within a quantum resource-theoretic framework, linking free energy dissipation to fluctuations during optimal thermodynamic distillation processes, applicable to large but finite systems.

Contribution

It introduces a quantum resource-theoretic derivation of fluctuation-dissipation relations for thermodynamic processes, including states with quantum coherence, and analyzes their performance in finite regimes.

Findings

Derived fluctuation-dissipation relations for quantum thermodynamic processes.

Characterized optimal distillation processes under thermodynamic constraints.

Analyzed performance of protocols like work extraction and information erasure for large finite systems.

Abstract

The fluctuation-dissipation theorem is a fundamental result in statistical physics that establishes a connection between the response of a system subject to a perturbation and the fluctuations associated with observables in equilibrium. Here we derive its version within a resource-theoretic framework, where one investigates optimal quantum state transitions under thermodynamic constraints. More precisely, we first characterise optimal thermodynamic distillation processes, and then prove a relation between the amount of free energy dissipated in such processes and the free energy fluctuations of the initial state of the system. Our results apply to initial states given by either asymptotically many identical pure systems or arbitrary number of independent energy-incoherent systems, and allow not only for a state transformation, but also for the change of Hamiltonian. The fluctuation-dissipation relations we derive enable us to find the optimal performance of thermodynamic protocols such as work extraction, information erasure and thermodynamically-free communication, up to second-order asymptotics in the number $N$ of processed systems. We thus provide a first rigorous analysis of these thermodynamic protocols for quantum states with coherence between different energy eigenstates in the intermediate regime of large but finite $N$.