Path integral approach to quantum thermodynamics

TL;DR

This paper introduces a novel path integral approach to quantum thermodynamics, defining a work functional along Feynman paths, enabling analysis of work statistics and quantum corrections in open quantum systems.

Contribution

It develops a new path integral framework for quantum thermodynamics, including a work functional and analytical derivation of work statistics and quantum-classical correspondence.

Findings

Derived a path-integral expression for work statistics.

Proved quantum-classical correspondence of work statistics.

Calculated quantum corrections to classical work.

Abstract

Work belongs to the most basic notions in thermodynamics but it is not well understood in quantum systems, especially in open quantum systems. By introducing a novel concept of work functional along individual Feynman path, we invent a new approach to study thermodynamics in the quantum regime. Using the work functional, we derive a path-integral expression for the work statistics. By performing the $\hbar$ expansion, we analytically prove the quantum-classical correspondence of the work statistics. In addition, we obtain the quantum correction to the classical fluctuating work. We can also apply this approach to an open quantum system in the strong coupling regime described by the quantum Brownian motion model. This approach provides an effective way to calculate the work in open quantum systems by utilizing various path integral techniques. As an example, we calculate the work statistics for a dragged harmonic oscillator in both isolated and open quantum systems.