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Energy flow in periodic thermodynamics

A key quantity characterizing a time-periodically forced quantum system coupled to a heat bath is the energy flowing in the steady state through the system into the bath, where it is dissipated. We derive a general expression which allows one to compute this energy dissipation rate for a heat bath consisting of a large number of harmonic oscillators, and work out two analytically solvable model examples. In particular, we distinguish between genuine transitions effectuating a change of the systems's Floquet state, and pseudo-transitions preserving that state; the latter are shown to yield an important contribution to the total dissipation rate. Our results suggest possible driving-mediated heating and cooling schemes on the quantum level. They also indicate that a driven system does not necessarily occupy only a single Floquet state when being in contact with a zero-temperature bath.