Anomalies, absence of local equilibrium and universality in 1-d particles systems

TL;DR

This paper investigates one-dimensional particle systems, revealing that they exhibit anomalous behaviors and lack local equilibrium, with properties influenced by microscopic dynamics and robust against parameter changes.

Contribution

It demonstrates that anomalous properties are typical in 1D systems and that chaos alone does not ensure local thermodynamic equilibrium.

Findings

Anomalous properties are common in 1D systems.

A linear relation exists between density fluctuations and temperature profiles.

Temporal asymmetry of fluctuations is robust to parameter modifications.

Abstract

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.