Non-equilibrium thermodynamics of quantum Brownian motion

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 spurious non-equilibrium currents lacking a clear physical interpretation. Our results highlight a fundamental tension between quantum consistency and thermodynamic equilibration in open quantum systems.