Stochastic Thermodynamics of Quantum-Induced Stochastic Dynamics

TL;DR

This work extends stochastic thermodynamics to semi-classical systems where a classical degree of freedom interacts with a quantum environment acting as a dynamic bath. By deriving a Generalized Langevin Equation from the Feynman-Vernon influence functional, it defines heat and work in a way that reveals the bath can both randomize motion and provide ordered energy via a deterministic drive. The entropy production is formulated through path probabilities, recovering the standard fluctuation-dissipation relation under equilibrium conditions, while non-equilibrium quantum features such as squeezing introduce a non-local correction that yields a modified Second Law with an effective bath temperature $T_{\text{eff}} \propto T \cosh(2r)$. The framework is demonstrated on a nanoparticle in a cavity, showing how quantum light can tune energy exchange and irreversibility, with potential applications to optomechanics and quantum-enhanced thermodynamic protocols.

Abstract

Quantum-Induced Stochastic Dynamics arises from the coupling between a classical system and a quantum environment. Unlike standard thermal reservoirs, this environment acts as a dynamic bath, capable of simultaneously exchanging heat and performing work. We formulate a thermodynamic framework for this semi-classical regime, defining heat, work, and entropy production. We derive a modified Second Law that accounts for non-equilibrium quantum features, such as squeezing. The framework is exemplified by an optomechanical setup, where we characterize the thermodynamics of the non-stationary noise induced by the cavity field.