CPTP extensions of quantum Brownian motion violate detailed balance at steady state, resulting in non-vanishing entropy production and non-equilibrium currents.
Vacchini, Quantum optical versus quantum brownian motion master equation in terms of covariance and equi- librium properties, Journal of Mathematical Physics 43, 5446 (2002)
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Broken Detailed Balance and Entropy Production in CPTP Quantum Brownian Motion
CPTP extensions of quantum Brownian motion violate detailed balance at steady state, resulting in non-vanishing entropy production and non-equilibrium currents.