Approach to equilibrium via Tsallis distributions in a realistic ionic--crystal model and in the FPU model

TL;DR

This paper demonstrates that Tsallis distributions appear in both realistic ionic-crystal models with long-range Coulomb forces and in the short-range FPU model, suggesting their occurrence is linked to non-fully chaotic dynamics rather than long-range interactions.

Contribution

It shows for the first time that Tsallis distributions occur in a realistic ionic-crystal model and in the FPU model, challenging the idea that long-range interactions are necessary for such distributions.

Findings

Tsallis distributions are observed in ionic-crystal models with Coulomb forces.

Tsallis distributions also occur in the short-range FPU model.

Presence of Tsallis distributions is linked to non-fully chaotic dynamics.

Abstract

In Statistical Mechanics, Tsallis distributions were apparently conceived in connection with systems presenting long--range interactions. In fact, they were observed in numerical computations for models of such a type, as occurring in the approach to equilibrium, i.e., to a Maxwell--Boltzmann distribution. Here we exhibit two apparently new results. The first one is that Tsallis distributions occur also in an ionic--crystal model with long--range Coulomb forces, which is so realistic as to reproduce in an impressively good way the experimental infrared spectra. Thus such distributions may be expected to be actual physical features of crystals. The second result is that Tsallis distributions occur in the standard short--range FPU model too, so that the presence of long--range interactions is not a necessary condition for Tsallis distributions to occur. In fact, this is in agreement with a previous result of the first author in connection with the statistics of return times for the classical FPU model. We thus confirm the thesis advanced by Tsallis himself, that the relevant property for a dynamical system to present Tsallis distributions is that its dynamics should be not fully chaotic, a property which is known to actually pertain to long--range systems.