Quantum Fokker-Planck-Kramers equation and entropy production

Abstract

We use a canonical quantization procedure to set up a quantum Fokker-Planck-Kramers equation that accounts for quantum dissipation in a thermal environment. The dissipation term is chosen to ensure that the thermodynamic equilibrium is described by the Gibbs state. An expression for the quantum entropy production is also provided which properly describes quantum systems in a nonequilibrium stationary state. The time-dependent solution is given for a quantum harmonic oscillator in contact with a heat bath. We also obtain the stationary solution for a system of two coupled harmonic oscillators in contact with reservoirs at distinct temperatures, from which we obtain the entropy production and the quantum thermal conductance.

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• Models for local ohmic quantum dissipation
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• On thermalization of two-level quantum systems
• Quantum Langevin equation
• Does canonical quantization lead to GKSL dynamics?
• Heat transport along a chain of coupled quantum harmonic oscillators
• Thermal conductance of a two-level atom coupled to two quantum harmonic oscillators
• Explicit noise and dissipation operators for quantum stochastic thermodynamics
• Unification of Stochastic and Quantum Thermodynamics in Scalar Field Theory via a Model with Brownian Thermostat
• A Nonlinear Master Equation for Open Quantum Systems
• Statistical Thermodynamics of the Fröhlich-Bose-Einstein Condensation of Magnons out of Equilibrium