Applications of periodic orbit theory to N-particle systems

In recent years a number of new techniques have become available in nonequilibrium statistical mechanics, all derived From dynamical system theory, especially From the thermodynamic formalism of Ruelle. We focus here on periodic orbit theory, and we compare it with a novel approach proposed by Evans, Cohen, and Morriss, and developed further by Gallavotti and Cohen. We argue that the two approaches based on such theories are equivalent for systems of many particles if the underlying dynamics is similar to that of Anosov systems, and that such equivalence should remain in more general situations. We extend our previous explanation of irreversibility in the thermostatted Lorentz gas to !V-particle diffusion and shearing systems.