Existence of time evolutions of non-equilibrium states in statistical mechanics (Q761711)

The author shows in the context of continuous infinite system statistical mechanics that under rather general conditions there exist time evolutions \(\mu^ t\) of states \(\mu\) which are the limits of time evolutions \(\mu^ t_{\Lambda}\) of finite volume ensembles \(\mu_{\Lambda}\) where the latter time evolutions are induced by finite volume flows \(T^ t_{\Lambda}\) such that \(\mu^ t_{\Lambda}(\cdot)=\mu_{\Lambda}(T^{-t}_{\Lambda}(\cdot)).\) The proof makes use of non-standard analysis and involves the construction of a very large ''infinite system phase space'' in an appropriate non-standard structure. The author arrives at results which generalize several previously known results obtained by ''standard'' methods.