Quantum-classical correspondence principle for heat distribution in quantum Brownian motion

Abstract

Quantum Brownian motion, described by the Caldeira-Leggett model, brings insights to understand phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum-classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat, and its long-time limit reflects complete thermalization of the system. Our research brings justification for the definition of the quantum fluctuating heat via two-point measurements.

32 pages, 2 figures

References in corpus (14)

• Fluctuation theorems: Work is not an observable
• Quantum Thermodynamics: A Nonequilibrium Green's Functions Approach
• Extended Heat-Fluctuation Theorems for a System with Deterministic and Stochastic Forces
• Work and heat probability distribution of an optically driven Brownian particle: Theory and experiments
• Symmetries of generating functionals of Langevin processes with colored multiplicative noise
• Functional Integral approach to time-dependent heat exchange in open quantum systems: general method and applications
• A field-theoretic approach to nonequilibrium work identities
• Calculating work in adiabatic two-level quantum Markovian master equations: A characteristic function method
• Heat distribution function for motion in a general potential at low temperature
• A microscopic theory of Curzon-Ahlborn heat engine
• Quantum thermal transport through anharmonic systems: A self-consistent approach
• Heat fluctuations in equilibrium
• Unifying quantum heat transfer in a nonequilibrium spin-boson model with full counting statistics
• Computing characteristic functions of quantum work in phase space

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• Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs
• Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold
• Effects of the kinetic energy in heat for overdamped systems