Quantum stochastic thermodynamics: A semiclassical theory in phase space

• URL: http://arxiv.org/abs/2303.05935v5
• Date: Sun, 3 Dec 2023 06:37:21 GMT
• Title: Quantum stochastic thermodynamics: A semiclassical theory in phase space
• Authors: Zhaoyu Fei
• Abstract summary: A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space. We use a Fokker-Planck equation as the dynamics at the mesoscopic level. We define thermodynamic quantities based on the trajectories of the phase-space distribution.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish a stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic Fokker-Planck equation as the dynamics at the mesoscopic level. Here, the noise term characterizing the fluctuation of the flux density accounts for the finite-$N$ effects of random collisions between the system and the reservoir. Accordingly, the stationary solution is a quasi-equilibrium state in a canonical system. We define stochastic thermodynamic quantities based on the trajectories of the phase-space distribution. The conservation law of energy, $H$ theorem and fluctuation theorems are therefore obtained. Our work sets an alternative formalism of quantum stochastic thermodynamics that is independent of the two-point measurement scheme. The numerous projective measurements of quantum systems are replaced by the sampling of the phase-space distribution, offering hope for experimental verifications in the future.

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