  We study the possibility of applying statistical mechanics to generally
covariant quantum theories with a vanishing Hamiltonian. We show that (under
certain appropiate conditions) this makes sense, in spite of the absence of a
notion of energy and external time. We consider a composite system formed by a
large number of identical components, and apply Boltzmann's ideas and the
fundamental postulates of ordinary statistical physics. The thermodynamical
parameters are determined by the properties of the thermalizing interaction. We
apply these ideas to a simple example, in which the component system has one
physical degree of freedom and mimics the constraint algebra of general
relativity.
