  The problem of time is an unsolved issue of canonical General Relativity. A
possible solution is the Brown-Kuchar mechanism which couples matter to the
gravitational field and recovers a physical, i.e. non vanishing, observable
Hamiltonian functional by manipulating the set of constraints. Two cases are
analyzed. A generalized scalar fluid model provides an evolutionary picture,
but only in a singular case. The Schutz' model provides an interesting
singularity free result: the entropy per baryon enters the definition of the
physical Hamiltonian. Moreover in the co-moving frame one is able to identify
the time variable tau with the logarithm of entropy.
