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A gauge-invariant C*-system is obtained as the fixed point subalgebra of theinfinite tensor product of full matrix algebras under the tensor productunitary action of a compact group. In the paper, thermodynamics is studied onsuch systems and the chemical potential theory developed by Araki, Haag,Kastler and Takesaki is used. As a generalization of quantum spin system, theequivalence of the KMS condition, the Gibbs condition and the variationalprinciple is shown for translation-invariant states. The entropy density ofextremal equilibrium states is also investigated in relation to macroscopicuniformity.Comment: 20 pages, revised in March 200

EQUILIBRIUM STATES AND THEIR ENTROPY DENSITIES IN GAUGE-INVARIANT C*-SYSTEMS