Non-equilibrium thermodynamics of the quantum Brownian motion: Anomalous non-equilibrium currents arising from complete positivity

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.

Simone Artini
Simone Artini
PhD Student
Gabriele Lo Monaco
Gabriele Lo Monaco
Assistant Professor
Mauro Paternostro
Mauro Paternostro
Full Professor