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Broken Detailed Balance and Entropy Production in CPTP Quantum Brownian Motion
arXiv:2507.23322v3 Announce Type: replace Abstract: We rigorously analyze the non-equilibrium thermodynamic behavior of various formulations of quantum Brownian motion (QBM) using the framework of stochastic thermodynamics. While the widely used Caldeira-Leggett master equation exhibits desirable thermodynamic features, such as the fulfilment of a detailed balance, it fails to ensure complete positivity. In contrast, several completely positive and trace-preserving (CPTP) extensions turn out to be thermodynamically controversial. We show that such extensions introduce anomalous phase-space structures that violate detailed balance at the steady state, leading to non-vanishing entropy production and effective non-equilibrium current of unclear physical origins. Our results highlight a fundamental tension between quantum consistency and thermodynamic equilibration in open quantum systems.
Abstract:We rigorously analyze the non-equilibrium thermodynamic behavior of various formulations of quantum Brownian motion (QBM) using the framework of stochastic thermodynamics. While the widely used Caldeira-Leggett master equation exhibits desirable thermodynamic features, such as the fulfilment of a detailed balance, it fails to ensure complete positivity. In contrast, several completely positive and trace-preserving (CPTP) extensions turn out to be thermodynamically controversial. We show that such extensions introduce anomalous phase-space structures that violate detailed balance at the steady state, leading to non-vanishing entropy production and effective non-equilibrium current of unclear physical origins. Our results highlight a fundamental tension between quantum consistency and thermodynamic equilibration in open quantum systems.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2507.23322 [quant-ph]
(or arXiv:2507.23322v3 [quant-ph] for this version)
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