  We discuss an application of group theoretical methods to the formulation of
the thermodynamics of systems constrained by the conservation laws described by
a semi--simple compact Lie group. A general projection method that allows to
construct a partition function for a given irreducible representation of the
Lie group is outlined. Applications of the method in Lattice Gauge Theory (LGT)
for non--zero baryon number and in the phenomenological description of particle
production in ultrarelativistic heavy ion collisions are also indicated.
