Invariant Measures in Generic Dynamical Systems

Irreversible thermodynamics of simple fluids have been connected recently to the theory of dynamical systems and some interesting assumptions have been made about the nature of the associated invariant measures. We show that the tests of validity of these assumptions are insufficient by exhibiting observables that are incorrectly sampled with the proposed invariant measures. Only observables belonging to the "high temperature phase" of the thermodynamic formalism are insensitive to the sampling methods. We outline methods that are free of these deficiencies.