Anomalies and absence of local equilibrium, and universality, in one-dimensional particles systems

One-dimensional systems are under intense investigation, both from theoretical and experimental points ofview, since they have rather peculiar characteristics which are of both conceptual and technological interest.We analyze the dependence of the behavior of one-dimensional, time-reversal invariant, nonequilibrium systemson the parameters defining their microscopic dynamics. In particular, we consider chains of identical oscillatorsinteracting via hard-core elastic collisions and harmonic potentials, driven by boundary Nos´e-Hoover thermostats.Their behavior mirrors qualitatively that of stochastically driven systems, showing that anomalous properties aretypical of physics in one dimension. Chaos, by itself, does not lead to standard behavior, since it does not guaranteelocal thermodynamic equilibrium.Alinear relation is found between density fluctuations and temperature profiles.This link and the temporal asymmetry of fluctuations of the main observables are robust against modifications ofthermostat parameters and against perturbations of the dynamics.