Broken Detailed Balance and Entropy Production in CPTP Quantum Brownian Motion
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.
Keywords
Cite
@article{arxiv.2507.23322,
title = {Broken Detailed Balance and Entropy Production in CPTP Quantum Brownian Motion},
author = {Simone Artini and Gabriele Lo Monaco and Alberto Imparato and Mauro Paternostro and Sandro Donadi},
journal= {arXiv preprint arXiv:2507.23322},
year = {2026}
}