Thermostatistics of Overdamped Motion of Interacting Particles

Abstract

We show through a nonlinear Fokker-Planck formalism, and confirm by molecular dynamics simulations, that the overdamped motion of interacting particles at T=0, where T is the temperature of a thermal bath connected to the system, can be directly associated with Tsallis thermostatistics. For sufficiently high values of T, the distribution of particles becomes Gaussian, so that the classical Boltzmann-Gibbs behavior is recovered. For intermediate temperatures of the thermal bath, the system displays a mixed behavior that follows a novel type of thermostatistics, where the entropy is given by a linear combination of Tsallis and Boltzmann-Gibbs entropies.

Possible Implication of a Single NonextensivepTDistribution for Hadron Production in High-EnergyppCollisions

“…What we may extract from the behavior of the experimental data is that scenario proposed in [11,12] appears to be essentially correct excepting for the fact that we are not facing thermal equilibrium but a different type of stationary state, typical of violation of ergodicity (for a discussion of the kinetic and effective temperatures see [55,56])).…”

What do Generalized Entropies Look Like? An Axiomatic Approach for Complex, Non-Ergodic Systems

“…particles diffuse normally, while at zero temperature the system is governed by Tsallis entropy with a non-Gaussian parabolic diffusion profile of compact support. The concrete stationary distribution functions given in [22] can be used to demonstrate that the system is found either in the asymptotic equivalence class (c, d) = (1, 1) (BG entropy) or in (c, d) = (1, 0) (compact support entropies) depending on the temperature of the heat bath. Expressing the integral by a discrete sum the entropy given in [22] can be used to demonstrate the existence of the two sets of classes.…”

“…The concrete stationary distribution functions given in [22] can be used to demonstrate that the system is found either in the asymptotic equivalence class (c, d) = (1, 1) (BG entropy) or in (c, d) = (1, 0) (compact support entropies) depending on the temperature of the heat bath. Expressing the integral by a discrete sum the entropy given in [22] can be used to demonstrate the existence of the two sets of classes. This shows that the classification is applicable for concrete physical systems and suggests further that the equivalence class (c, d) may even depend on macro variables of the system such as the temperature of the heat bath.…”

“…For details see [22], where the non-linear Fokker-Planck equation for the spatial distribution ρ(x) of the particles was solved. It was shown that the corresponding entropy is a superposition of BG and Tsallis entropy with q = 2.…”

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.…”