Fluttuazioni in sistemi fuori dall'equilibrio e reversibilità temporale

My master thesis deals with the study of nonequilibrium systems from the point of view of dissipative dynamical system theory. In particular, it focuses on the fluctuation relations which are symmetry relations concerning the statistic of time averages for an ensemble of systems arbitrarly far from equilibrium. By means of the dissipation function formalism, it is possible to derive the fluctuation relations without the need of any stringent mathematical hypothesis on the dynamics (Anosov system). The only ingredient necessary to this derivation is time reversal invariance (TRI). A system is said to be time reversal invariant if there exists an involution acting on the phase space which, combined with the inversion of time, leaves the equation of motion invariant. In the first part of my work a generalized fluctuation relation under time-dependent perturbation has been proposed. At this scope, the theory of the dissipation function has been developed in presence of a periodic perturbation through the embedding of the phase space into a larger one and the dissipation formula in the expanded phase space has been derived. Secondly, I focused on two classes of systems commonly thought to violate TRI for which a generalized reversal operator has recently been discovered. These are the cases of a system in a rotating reference frame or subject to a constant magnetic field. The latter case opens up the possibility to investigate symmetry properties, such as fluctuation relations as well as Green Kubo relations, in presence of a magnetic field. At this scope, a molecular dynamics approach has been introduced and some preliminary calculations on the time symmetry properties of the intermediate scattering function have been performed.