Influence of the interaction range on the thermostatistics of a classical many-body system

Abstract

We numerically study a one-dimensional system of N classical localized planar rotators coupled through interactions which decay with distance as 1/r α (α ≥ 0). The approach is a first principle one (i.e., based on Newton's law), and yields the probability distribution of momenta. For α large enough and N ≫ 1 we observe, for longstanding states, the Maxwellian distribution, landmark of Boltzmann-Gibbs thermostatistics. But, for α small or comparable to unity, we observe instead robust fat-tailed distributions that are quite well fitted with q-Gaussians. These distributions extremize, under appropriate simple constraints, the nonadditive entropy S q upon which nonextensive statistical mechanics is based. The whole scenario appears to be consistent with nonergodicity and with the thesis of the q-generalized Central Limit Theorem.

Fermi-Pasta-Ulam model with long-range interactions: Dynamics and thermostatistics

“…proportional to N ) for all values of α. We note that the above scaling N (N, α) applies to lattices with fixed boundary conditions and is only slightly different from the analogous scaling found in [8,7] meant for periodic boundary conditions (PBC).…”

“…We note here that a significant difference of the present study from the generalized HMF model [8,9,7] lies in the implementation of long range interactions only in the quartic part of the potential in (1) (the introduction of long-range interactions also in the quadratic term leads to similar results and will be addressed elsewhere). Our numerical results are obtained using the 4-th order Yoshida symplectic scheme with time-step such that the energy is conserved within 4 to 5 significant digits.…”

On the putative essential discreteness of q-generalized entropies

“…Finally, we cite some recent works that successfully deal with the Tsallis' q-statistics with continuous probability distributions [26,27,28].…”

Nonextensive statistical mechanics and high energy physics

“…We briefly mention here some selected ones: cold atoms in optical lattices [17], trapped ions [18], asteroid motion and size [19], motion of biological cells [20], edge of chaos [21][22][23][24][25][26][27][28][29][30][31], restricted diffusion [32], defect turbulence [33], solar wind [34], dusty plasma [35,36], spin-glass [37], overdamped motion of interaction particles [38], tissue radiation [39], nonlinear relativistic and quantum equations [40], large deviation theory [41], long-range-interacting classical systems [42][43][44][45][46], microcalcification detection techniques [47], ozone layer [48], scale-free networks [49][50][51], among others.…”