  One dimensional systems are under intense investigation, both from
theoretical and experimental points of view, since they have rather peculiar
characteristics which are of both conceptual and technological interest. We
analyze the dependence of the behaviour of one dimensional, time reversal
invariant, nonequilibrium systems on the parameters defining their microscopic
dynamics. In particular, we consider chains of identical oscillators
interacting via hard core elastic collisions and harmonic potentials, driven by
boundary Nos\'e-Hoover thermostats. Their behaviour mirrors qualitatively that
of stochastically driven systems, showing that anomalous properties are typical
of physics in one dimension. Chaos, by itslef, does not lead to standard
behaviour, since it does not guarantee local thermodynamic equilibrium. A
linear 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 of thermostat parameters and against
perturbations of the dynamics.
