A thermodynamically consistent Markovian master equation beyond the secular approximation

Markovian master equations provide a versatile tool for describing open quantum systems whenmemory effects of the environment may be neglected. As these equations are of an approximatenature, they often do not respect the laws of thermodynamics when no secular approximation isperformed in their derivation. Here we introduce a Markovian master equation that isthermodynamically consistent and provides an accurate description whenever memory effects canbe neglected. The thermodynamic consistency is obtained through a rescaled Hamiltonian for thethermodynamic bookkeeping, exploiting the fact that a Markovian description implies a limitedresolution for heat. Our results enable a thermodynamically consistent description of a variety ofsystems where the secular approximation breaks down.