Relaxation times and ergodic properties in a realistic ionic-crystal model, and the modern form of the FPU problem

Andrea Carati, Luigi Galgani, Fabrizio Gangemi and Roberto Gangemi

Physica A: Statistical Mechanics and its Applications, 2019, vol. 532, issue C

Abstract: It is well known that Gibbs’ statistical mechanics is not justified for systems presenting long-range interactions, such as plasmas or galaxies. In a previous work we considered a realistic FPU-like model of an ionic crystal (and thus with long-range interactions), and showed that it reproduces the experimental infrared spectra from 1000 K down to 7 K, provided one abandons the Gibbs identification of temperature in terms of specific kinetic energy, at low temperatures. Here we investigate such a model in connection with its ergodic properties. The conclusion we reach is that at low temperatures ergodicity does not occur, and thus the Gibbs prescriptions are not dynamically justified, up to geological time scales. We finally give a preliminary result indicating how the so-called “nonclassical” q-statistics show up in the realistic ionic-crystal model. How to formulate a consistent statistical mechanics, with the corresponding suitable identification of temperature in such nonergodicity conditions, remains an open problem, which apparently constitutes the modern form of the FPU problem.

Keywords: Relaxation times; Ergodicity; Ionic crystal model; Long-range interactions; FPU problem (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:532:y:2019:i:c:s0378437119311240

DOI: 10.1016/j.physa.2019.121911

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