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We report the results of a numerical investigation, performed in the frame ofdynamical systems' theory, for a realistic model of a ionic crystal for which,due to the presence of long--range Coulomb interactions, the Gibbs distributionis not well defined. Taking initial data with a Maxwell-Boltzmann distributionfor the mode-energies $E_k$, we study the dynamical fluctuations, computing themoduli of the the energy-changes $|E_k(t)-E_k(0)|$. The main result is thatthey follow Tsallis distributions, which relax to distributions close toMaxwell-Boltzmann ones; indications are also given that the system remainscorrelated. 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 curvehas 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 $\Delta t$ therelaxation time $\tau$, the relation reads $\Delta t \cdot \Delta E \simeq h$,which reminds of the Heisenberg uncertainty relation. Moreover, the thresholdcorresponds 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 discrepancyof a factor 2. So it seems that lack of full chaoticity manifests itself, inStatistical Thermodynamics, through quantum-like phenomena.

Tsallis distributions, their relaxations and the relation $\Delta t  \cdot \Delta E \simeq h$, in the dynamical fluctuations of a classical model  of a crystal