Quantum mechanics

Lindblad equation

Balance (ability)

Classical mechanics

Second law of thermodynamics

Statistical physics

Physics

Mathematics

Detailed balance

Conservation law

Geometry

Conservation of energy

Quantum

Medicine

Physical medicine and rehabilitation

Master equation

Consistency (knowledge bases)

Physical review. A/Physical review, A

Starting from a microscopic system-baths description, we derive the general conditions for a time-local quantum master equation (QME) to satisfy the first and second laws of thermodynamics at the fluctuating level. Using counting statistics, we show that the fluctuating second law can be rephrased as a generalized quantum detailed balance condition (GQDB), i.e., a symmetry of the time-local generators which ensures the validity of the fluctuation theorem. When requiring in addition a strict system-bath energy conservation, the GQDB reduces to the usual notion of detailed balance which characterizes QMEs with Gibbsian steady states. However, if energy conservation is only required on average, QMEs with non-Gibbsian steady states can still maintain a certain level of thermodynamic consistency. Applying our theory to commonly used QMEs, we show that the Redfield equation breaks the GQDB, and that some recently derived approximation schemes based on the Redfield equation (which hold beyond the secular approximation and allow one to derive a QME of Lindblad form) satisfy the GQDB and the average first law. We find that performing the secular approximation is the only way to ensure the first and second laws at the fluctuating level.

Thermodynamic consistency of quantum master equations