Statistical treatment of autonomous systems with divergencelless flows

Statistical Mechanics (SM) has been quite successful in providing one with exact, or at least approximate, descriptions of the time-dependent solutions of the Liouville (or of the von Neumann) equation within the context of Hamiltonian dynamics (HD). Here we investigate how to extend some of its ideas to more general dynamical systems. We find that for systems that retain from HD just the divergenceless character of the phase space flow many ideas borrowed from the Maximum Entropy Principle approach to SM apply in such a generalized context as well.