Path integral approach to heat in quantum thermodynamics

TL;DR

This paper introduces a path integral method to analyze heat in quantum thermodynamics, defining a quantum heat functional along Feynman paths, and explores its properties and classical correspondence.

Contribution

It presents a novel path integral framework with a quantum heat functional, enhancing understanding of heat in quantum systems and its relation to classical thermodynamics.

Findings

Demonstrates microscopic reversibility via heat functional

Proves quantum-classical correspondence of heat statistics

Provides analytical insights into quantum heat behavior

Abstract

We study the heat statistics of a quantum Brownian motion described by the Caldeira-Leggett model. By using the path integral approach, we introduce a novel concept of the quantum heat functional along every pair of Feynman paths. This approach has an advantage of improving our understanding about heat in quantum systems. First, we demonstrate the microscopic reversibility of the system by connecting the heat functional to the forward and its time-reversed probabilities. Second, we analytically prove the quantum-classical correspondence of the heat functional and their statistics, which allows us to obtain better intuitions about the difference between classical and quantum heat.