Stochastic Thermodynamics of Quantum-Induced Stochastic Dynamics

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.

💡 Research Summary

The manuscript introduces a thermodynamic framework for “Quantum‑Induced Stochastic Dynamics” (QISD), a regime where a classical degree of freedom acquires stochastic motion solely through its coupling to a quantum environment. Unlike a conventional thermal reservoir, the quantum bath can simultaneously provide random fluctuations (heat), dissipative friction, and a deterministic drive when prepared in a coherent or squeezed state. The authors start by writing the total density matrix evolution ρ̂_tot(t)=Û(t)ρ̂_0Û†(t) and tracing out the quantum subsystem B to obtain the reduced density matrix of the classical system A. Using the Feynman‑Vernon influence functional, they express the reduced dynamics in terms of a noise kernel K(t,t′) (decoherence) and a dissipation kernel D(t,t′) (back‑action). Assuming a quadratic (Gaussian) influence functional, they introduce center‑of‑mass x(t) and coherence y(t) coordinates, then take the classical limit y→0, which collapses the path integral into a Wiener measure. This yields a generalized Langevin equation (GLE):

 m ¨x(t)+∂_xV(x)=F_diss(t)+η(t)+F_det(t),

where η(t) is a zero‑mean Gaussian colored noise with ⟨η(t)η(t′)⟩=K(t,t′) and F_diss(t)=−∫_0^t D(t,t′)·ẋ(t′)dt′. The deterministic term F_det(t) appears when the quantum bath is in a non‑thermal (e.g., coherent) state and acts as an external control parameter.

With the stochastic dynamics in hand, the authors define stochastic work and heat. Work is associated with the deterministic drive:

 W