EQUIVALENCE OF NONEQUILIBRIUM ENSEMBLES FOR SIMPLE MAPS

In this paper we discuss the equivalence of different approaches to th e same transport problems, with particular attention to recent works b y Breyman et al. These suggest a singular equivalence between the stat ionary states of models from Gaussian dynamics, and those from chaotic scattering theory. Although, the mentioned equivalence may concern bu t a limited set of the properties of those systems, it is very importa nt from a theoretical standpoint. We argue that a special form of diss ipativity, in the evolution equations of the phase space distributions , is to be invoked to understand those facts. We discuss one applicati on of periodic orbit theory, to illustrate how the stationary states o f thermostatted systems can be investigated and some qualitative featu res obtained.