Broken Detailed Balance and Entropy Production in CPTP Quantum Brownian Motion

TL;DR

This paper investigates the thermodynamic properties of quantum Brownian motion, revealing that CPTP extensions can violate detailed balance and produce non-physical entropy production, highlighting a tension between quantum consistency and thermodynamics.

Contribution

It provides a rigorous analysis of different QBM formulations, showing how CPTP extensions can introduce thermodynamic anomalies and violate detailed balance.

Findings

Caldeira-Leggett master equation satisfies detailed balance but lacks complete positivity.

CPTP extensions can violate detailed balance and produce non-zero entropy production.

Anomalous phase-space structures are responsible for thermodynamic inconsistencies.

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.