Finite temperature Lewisʹ invariants for the Liouville equation

Invariants of the Lewis kind are introduced within the context of Statistical Mechanics via information theory concepts. Several invariants of the Liouville equation are in this way built-up. Both the classical and the quantal cases are studied. Some applications are discussed. It is shown that the celebrated Lewis invariants for the time-dependent harmonic oscillator are but special cases of our more general invariants.