  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.
