We give an example of a statistical model which describes the exchange of energy among the normal modes of a generally designed physical system.The thermodynamic properties are computed in detail, as well as some generalizations.The main result concerns the independence of the entropy density on the presence of energy conservation laws.This makes the result applicable to both conservative and dissipative cases.The most probable distribution is computed using the Darwin-Fowler method.Finite volume corrections are also given.An appendix is devoted to the use of our formula for the entropy density to analyze experimental data on mode amplitude fluctuations in Rayleigh-Benard convection in an annulus.