Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relaxation times and ergodicity properties in a realistic ionic--crystal
  model, and the modern form of the FPU problem   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
ergodicity 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.

11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas