  We report the results of a numerical investigation, performed in the frame of
dynamical systems' theory, for a realistic model of a ionic crystal for which,
due to the presence of long--range Coulomb interactions, the Gibbs distribution
is not well defined. Taking initial data with a Maxwell-Boltzmann distribution
for the mode-energies $E_k$, we study the dynamical fluctuations, computing the
moduli of the the energy-changes $|E_k(t)-E_k(0)|$. The main result is that
they follow Tsallis distributions, which relax to distributions close to
Maxwell-Boltzmann ones; indications are also given that the system remains
correlated. The relaxation time $\tau$ depends on specific energy
$\varepsilon$, and for the curve $\tau$ vs, $\varepsilon$ one has two results.
First, there exists an energy threshold $\varepsilon_0$, above which the curve
has the form $$
  \tau \cdot \varepsilon \simeq h\ , $$ where, unexpectedly, Planck's constant
$h$ shows up. In terms of the standard deviation $\Delta E$ of a mode-energy
(for which one has $\Delta E=\varepsilon$), denoting by $\Delta t$ the
relaxation time $\tau$, the relation reads $\Delta t \cdot \Delta E \simeq h$,
which reminds of the Heisenberg uncertainty relation. Moreover, the threshold
corresponds to zero-point energy. Indeed, the quantum value of the latter is
$h\nu/2$ ( where $\nu$ is the characterisic infrared frequency of the system),
while we find $\varepsilon \simeq h\nu/4$, so that one only has a discrepancy
of a factor 2. So it seems that lack of full chaoticity manifests itself, in
Statistical Thermodynamics, through quantum-like phenomena.
