Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics.

*(English)*Zbl 0934.37010Summary: This paper reviews various applications to the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mechanics. The author adopts 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. At equilibrium one recovers in particular the Onsager reciprocity relations. 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.

##### MSC:

37A60 | Dynamical aspects of statistical mechanics |

37C99 | Smooth dynamical systems: general theory |

82C05 | Classical dynamic and nonequilibrium statistical mechanics (general) |