Quantum corrections to the entropy in a driven quantum Brownian motion model

Abstract

Quantum Brownian motion model is a typical model in the study of nonequilibrium quantum thermodynamics. Entropy is one of the most fundamental physical concepts in thermodynamics. In this work, by solving the quantum Langevin equation, we study the von Neumann entropy of a particle undergoing quantum Brownian motion. In both the strong and the weak coupling regimes, we obtain the analytical expression of the time evolution of the Wigner function in terms of the initial Wigner function. The result is applied to the thermodynamic equilibrium initial state, which reproduces its classical counterpart in the high-temperature limit. Based on these results, for those initial states having well-defined classical counterparts, we obtain the explicit expression of the quantum corrections to the entropy of the system. Moreover, under the Markovian approximation, we obtain the expression of the quantum corrections to the total entropy production rate $e_{\mathrm{p}}$ and the heat dissipation rate $h_{\mathrm{d}}$. Our results bring important insights to the understanding of entropy in open quantum systems.

References in corpus (41)

• Entropy production along a stochastic trajectory and an integral fluctuation theorem
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Quantum Thermodynamic Cycles and quantum heat engines
• Steady State Thermodynamics of Langevin Systems
• Fluctuation theorems: Work is not an observable
• A nano heat engine beyond the Carnot limit
• How small can thermal machines be? The smallest possible refrigerator
• Entropy production as correlation between system and reservoir
• Three detailed fluctuation theorems
• The Three Faces of the Second Law: I. Master Equation Formulation
• Fundamental Aspects of Quantum Brownian Motion
• Quantum mechanical Carnot engine
• The Three Faces of the Second Law: II. Fokker-Planck Formulation
• The Physical Origins of Entropy Production, Free Energy Dissipation and their Mathematical Representations
• Fluctuation theorem in quantum heat conduction
• Otto refrigerator based on a superconducting qubit: classical and quantum performance
• Alternative Derivation of the Hu-Paz-Zhang Master Equation for Quantum Brownian Motion
• A Quantum Fluctuation Theorem
• Exact solution of the Hu-Paz-Zhang master equation
• Scaling-up quantum heat engines efficiently via shortcuts to adiabaticity
• Wave Function Evolution of a Dissipative System
• Mesoscopic Nonequilibrium Thermodynamics of Single Macromolecules and Dynamic Entropy-Energy Compensation
• Optimal refrigerator
• The Wigner Entropy Production Rate
• Path integral approach to quantum thermodynamics
• Fluctuation relations for a driven Brownian particle
• Information and entropy in quantum Brownian motion: Thermodynamic entropy versus von Neumann entropy
• Entropy Production in Quantum Brownian Motion
• Quantum thermodynamics from the nonequilibrium dynamics of open systems: energy, heat capacity and the third law
• Work measurement in an optomechanical quantum heat engine
• Path integral approach to heat in quantum thermodynamics
• Thermodynamics of quantum Brownian motion with internal degrees of freedom: the role of entanglement in the strong-coupling quantum regime
• Fluctuation-Dissipation Relation from the Nonequilibrium Dynamics of a Nonlinear Open Quantum System
• On work and heat in time-dependent strong coupling
• Exact dynamics of driven Brownian oscillators
• Non-adiabatic entropy production for non-Markov dynamics
• A Classical Bound on Quantum Entropy
• von Neumann entropy and the entropy production of a damped harmonic oscillator
• Nonequilibrium Nonlinear Open Quantum Systems I. Functional Perturbative Analysis of a Weakly Anharmonic Oscillator
• Quantum corrections to the entropy and its application in the study of quantum Carnot engines

Cited by in corpus (4)

• Open quantum system dynamics and the mean force Gibbs state
• Quantum-classical correspondence principle for heat distribution in quantum Brownian motion
• Exact density matrix elements for a driven dissipative system described by a quadratic Hamiltonian
• Over forty years of research towards the understanding of Quantum Brownian Motion -- the contributions of A. O. Caldeira