On the von Neumann entropy of a bath linearly coupled to a driven quantum system

TL;DR

This paper calculates the von Neumann entropy change of harmonic oscillators coupled to a driven quantum system using the Feynman-Vernon formalism, bridging quantum and classical thermodynamics.

Contribution

It adapts the influence functional approach to quantify quantum entropy production in a driven system coupled to a bath, connecting quantum and classical thermodynamic descriptions.

Findings

Quantum entropy change expressed as expectation of three path functionals.

In the classical limit, these functionals reduce to known thermodynamic quantities.

Identifies a new boundary term in the classical limit.

Abstract

The change of the von Neumann entropy of a set of harmonic oscillators initially in thermal equilibrium and interacting linearly with an externally driven quantum system is computed by adapting the Feynman-Vernon influence functional formalism. This quantum entropy production has the form of the expectation value of three functionals of the forward and backward paths describing the system history in the Feynman-Vernon theory. In the classical limit of Kramers-Langevin dynamics (Caldeira-Leggett model) these functionals combine to three terms, where the first is the entropy production functional of stochastic thermodynamics, the classical work done by the system on the environment in units of $k_BT$, the second another functional with no analogue in stochastic thermodynamics, and the third is a boundary term.