David Ruelle

NONEQUILIBRIUM SEEN FROM A DYNAMICAL SYSTEMS VIEWPOINT:

SRB MEASURES, LINEAR RESPONSE, etc.

We shall first outline the diversity of physical situations and mathematical idealizations that go under the name of nonequilibrium. Then, we shall focus on nonequilibrium steady states (NESS) for classical systems with a finite number of degrees of freedom and a deterministic thermostat. From a mathematical point of view this means that we shall have to study the ergodic theory of differentiable dynamical systems on a (compact) manifold M. The discussion will involve isokinetik thermostatting, uniform hyperbolicity (=chaotic hypothesis), SRB states (=NESS), volume contraction (=entropy production), linear response and fluctuation theorems. We shall also consider the ”close to equilibrium”

situation, and ask what effects may be associated with lack of uniform hyperbolicity.