Path integral approach to the calculation of the characteristic function of work

TL;DR

This paper employs Feynman's path-integral method to analytically calculate work distributions in quantum and classical systems, providing a new approach that simplifies non-equilibrium thermodynamics analysis.

Contribution

It introduces a path-integral framework for work statistics, demonstrating its effectiveness and equivalence to traditional methods in quantum and classical thermodynamics.

Findings

Derived analytical work distributions for prototype quantum systems.

Proved equivalence of path-integral results with Schrödinger formalism.

Extended the approach to classical counterparts, showing broad applicability.

Abstract

Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work statistics in quantum systems by employing Feynman's path-integral approach. We derive the analytical work distributions of two prototype quantum systems. The results are proved to be equivalent to the results obtained based on Schr\"{o}dinger's formalism. We also calculate the work distributions in their classical counterparts by employing the path-integral approach. Our study demonstrates the effectiveness of the path-integral approach to the calculation of work statistics in both quantum and classical thermodynamics, and brings important insights to the understanding of the trajectory work in quantum systems.