Temporal asymmetry of fluctuations in the nonequilibrium FPU model

The large deviation theory recently developed by Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim is meant to extend the Onsager–Machlup theory to nonequilibrium phenomena, and predicts that the fluctuations of densities and currents in certain stochastic processes are not symmetric with respect to the time reversal operation. In this paper, several notions of fluctuations are introduced for deterministic systems, and it is observed that temporally asymmetric (not necessarily large) fluctuations are ubiquitous, even in the context of time reversal invariant dynamics of particle systems, in nonequilibrium states. To illustrate these ideas, the nonequilibrium FPU chain devised by Lepri, Livi and Politi is studied in detail.