  This paper reviews various applications of the theory of smooth dynamical
systems to conceptual problems of nonequilibrium statistical mechanics. We
adopt a new point of view which has emerged progressively in recent years, and
which takes seriously into account the chaotic character of the microscopic
time evolution. The emphasis is on nonequilibrium steady states rather than the
traditional approach to equilibrium point of view of Boltzmann. The
nonequilibrium steady states, in presence of a Gaussian thermostat, are
described by SRB measures. In terms of these one can prove the Gallavotti-Cohen
fluctuation theorem. One can also prove a general linear response formula and
study its consequences, which are not restricted to near equilibrium
situations. Under suitable conditions the nonequilibrium steady states satisfy
the pairing theorem of Dettmann and Morriss. The results just mentioned hold so
far only for classical systems; they do not involve large size, i.e., they hold
without a thermodynamic limit.
