The CH allows to represent as a standard stochastic process (one dimensional “Gibbs states”) the stationary states (in equilibrium and out of it). Therefore it is natural to ask whether the universality of the representation of the SRB distributions, for CH-complying stationary non-equilibrium states, can be translated into universal laws. The first candidates for such search are properties of the fluctuations statistical properties, which can be expected to inherit properties of the system is studied. Certainly the first question is the compatibility between irreversibility and microscopic reversibility. Help comes from the simulations: since the eighties reversible models for irreversible phenomena have been designed and studied. And questions have been debated like how is reversibility reflected on the properties of, say, transport coefficients, which are constants in the corresponding irreversible models. The question admits a rather general answer in the “fluctuation theorem”, which gives some light on the statistics of the phase space contraction (i.e. on the statistics of the rate of heat delivered to the thermostats, Sect.  2.2 ). Or, still in reversible models of stationary non-equilibrium states, it allows a general answer to the relation, at stationarity, between the probability in a stationary state of an event in which, in a given time, a given observable evolves following a given path and the probability that it evolves following the reversed path. The answer is that the two probabilities are the same if conditioned to an opposite value of the average rate of entropy production (identified with the rate of phase space contraction). The fluctuation theorem can also be related to simple extensions of Onsager’s reciprocity and Green-Kubo formulae. Finally, an attempt is made towards an application of the above ideas to quantum systems.