  A model for the thermodynamics of a quantum heat bath is introduced. Under
the assumption that the bath molecules have finitely many degrees of freedom
and are weakly interacting, we present a general derivation of the equation of
state of the bath in the thermodynamic limit. The relation between the
temperature and the specific energy of the bath depends on (i) the spectral
properties of the molecules, and (ii) the choice of probability measure on the
state space of a representative molecule. The results obtained illustrate how
the microscopic features of the molecular constituents determine the
macroscopic thermodynamic properties of the bath. Our findings can thus be used
to compare the merits of different hypotheses for the equilibrium states of
quantum systems. Two examples of plausible choices for the probability measure
are considered in detail.
