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

Abstract

We report results of dynamical simulations exhibiting the occurrence of Tsallis distributions, and their eventual approach to Maxwell–Boltzmann distributions, for the normal-mode energies of FPU-like systems. The first result is that Tsallis distributions occur 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. So, such distributions may be expected to represent actual physical features of crystals. The second result is that Tsallis distributions for the normal mode energies occur in the classical FPU model too. This is in agreement with previous results obtained in the latter model, namely: by Antonopoulos, Bountis and Basios for the distributions of local observables (particles’ properties as energies or momenta), and by the first of the present authors for the statistical properties of return times. All such results thus confirm the thesis advanced by Tsallis himself, i.e., 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, in particular, to systems with long-range interactions.