Irreversibility, the time arrow and a dynamical proof of the second law of thermodynamics

We provide a dynamical proof of the second law of thermodynamics, along the lines of an argument of Penrose and Gibbs, making crucial use of the upper semicontinuity of the mean entropy proved by Robinson and Ruelle and Lanford and Robinson. An example is provided by a class of models of quantum spin systems introduced by Emch and Radin. Consequences regarding irreversibility and the time arrow, as well as possible extensions to quantum continuous systems are discussed.