  We study probability distribution of a steady state of a periodically driven
system coupled to a thermal bath by using a quantum master equation in the weak
coupling limit. It is proved that, even when the external field is strong, the
probability distribution is independent of the detailed nature of the thermal
bath under the following conditions: (i) the Hamiltonian of the relevant system
is bounded and the period of the driving field is short, (ii) the Hamiltonians
for the driving field at different times commute, and (iii) the Hamiltonians of
the driving field and of the interaction between the relevant system and the
thermal bath commute. It is shown that the steady state is described by the
Gibbs distribution of the Floquet states of the relevant system at the
temperature of the thermal bath.
