  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.
