On K.M.S. evolutions and liouville in quantum statistical mechanics.

Statistical mechanics is the study of macroscopic properties of large systems starting from the microscopic properties. A system in a box is inadequate as a model for large systems since it presupposes the unphysical fiction of a completely isolated system. For instance a system in a box neither exhibits phase transitions (cf. [ l ] theory of Yang and Lee) nor approach to equilibriumn (cf. [ l ] poincaré cycle), both well known phenomena for physicalsystems. To reproduce the thermodynamic behaviour one performs the so-called thermodynamic limit, i.e. one uses the "Gibbs Ansatz" to calculate the expectation values of observables and takes the limit V (volume), N (number of parcicles), keeping N/V fixed. ... Zie: Summary