Transient exchange fluctuation theorems for heat using Hamiltonian framework: Classical and Quantum

TL;DR

This paper derives and generalizes transient heat fluctuation theorems for classical and quantum systems using Hamiltonian dynamics, including multiple heat baths and quantum measurement effects.

Contribution

It provides a Hamiltonian-based analytical derivation of heat fluctuation theorems in the transient regime for both classical and quantum systems, extending previous results.

Findings

Exact agreement with known classical results

Generalization to multiple heat baths

Extension to quantum systems using von Neumann measurements

Abstract

We investigate the statistics of heat exchange between a finite system coupled to reservoir(s). We have obtained analytical results for heat fluctuation theorem in the transient regime considering the Hamiltonian dynamics of the composite system consisting of the system of interest and the heat bath(s). The system of interest is driven by an external protocol. We first derive it in the context of a single heat bath. The result is in exact agreement with known result. We then generalize the treatment to two heat baths. We further extend the study to quantum systems and show that relations similar to the classical case hold in the quantum regime. For our study we invoke von Neumann two point projective measurement in quantum mechanics in the transient regime. Our result is a generalisation of Jarzynski-W$\grave{o}$jcik heat fluctuation theorem.