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Broken detailed balance and entropy production in completely positive and trace-preserving quantum Brownian motion

Simone Artini1,*, Gabriele Lo Monaco1, Alberto Imparato2,3, Mauro Paternostro1,4, and Sandro Donadi2,3

  • *Contact author: simone.artini@unipa.it
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Phys. Rev. Research 8, 033216 – Published 21 August, 2026

DOI: https://doi.org/10.1103/qqxn-qc4g

Abstract

We rigorously analyze the nonequilibrium thermodynamic behavior of various formulations of quantum Brownian motion using the framework of stochastic thermodynamics. While the widely used Caldeira-Leggett master equation exhibits desirable thermodynamic features—such as the fulfillment of a detailed balance—it fails to ensure complete positivity. In contrast, several completely positive and trace-preserving 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 nonvanishing entropy production and spurious nonequilibrium currents lacking a clear physical interpretation. Our results highlight a fundamental tension between quantum consistency and thermodynamic equilibration in open quantum systems.

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Phys. Rev. Research 8, 033216– Published 21 August, 2026
  • Received 17 September 2025
  • Revised 3 April 2026
  • Accepted 17 July 2026
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