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The coarse-graining approach to deriving the quantum Markovian masterequation is revisited, with close attention given to the underlyingapproximations. It is further argued that the time interval over which thecoarse-graining is performed is a free parameter that can be given a physicalmeasurement-based interpretation. In the case of the damping of compositesystems to reservoirs of different temperatures, currently of much interest inthe study of quantum thermal machines with regard to the validity of `local'and `global' forms of these equations, the coupling of the subsystems leads toa further timescale with respect to which the coarse-graining time interval canbe chosen. Different choices lead to different master equations that correspondto the local and global forms. These can be then understood as having differentphysical interpretations based on the role of the coarse-graining, as well asdifferent limitations in application.

Coarse-graining in the derivation of Markovian master equations and its significance in quantum thermodynamics