  It was recently shown that the experimental infrared spectra of ionic
crystals at room temperature are very well reproduced by classical realistic
models, and here new results are reported on the temperature dependence of the
spectra, for the LiF crystal. The principal aim of the present work is however
to highlight the deep analogy existing between the problem of spectra in ionic
crystal models on the one hand, and that of energy equipartition in the
Fermi--Pasta--Ulam model, on the other. Indeed at low temperatures the
computations of the spectra show that the dynamics of the considered system is
not completely chaotic, so that the use of the Boltzmann--Gibbs statistics is
put in question, as in the Fermi--Pasta--Ulam case. Here, however, at variance
with the equipartition problem, a first positive indication is given on the
modifications that should be introduced in a classical statistical treatment:
the new results at low temperatures show that it is indeed the Clausius
identification of temperature that has to be modified. In fact, at very low
temperatures the theoretical spectra fail to reproduce the experimental ones,
if the temperature is taken as proportional to mean kinetic energy, but
agreement is recovered through the only expedient of introducing a suitable
temperature rescaling. Analogous results are also found in connection with
thermal expansion.
