We briefly review, with regard to physical applications, the present status of the recently introduced non-extensive thermostatistics characterized by the entropic index q (q = 1 corresponds to standard, extensive, Boltzmann-Gibbs thermostatistics). In addition to that, we comment on (i) how...

Increasing the number N of elements of a system typically makes the entropy to increase. The question arises on what particular entropic form we have in mind and how it increases with N. Thermodynamically speaking it makes sense to choose an entropy which increases linearly with N for large N,...

We carry on computer simulations in order to discuss the maintenance of polygenic variance in a model with migrating finite diploid population, non-overlapping generations and non-random mating, submitted to stabilizing selection and to spontaneous mutations. We sweep a wide spectrum of mutation...

The experimental formation factor (F) vs. porosity (φ) as well as resistivity index (I) vs. water saturation (Sw) results typically present, in double-logarithmic representation, bendings which we now interpret as crossovers between different fractal-like regimes. We consistently propose for...

We consider probabilistic models of N identical distinguishable, binary random variables. If these variables are strictly or asymptotically independent, then, for N→∞, (i) the attractor in distribution space is, according to the standard central limit theorem, a Gaussian, and (ii) the...

The analytical and computational studies of various isolated classical Hamiltonian systems including long-range interactions suggest that the N→∞ and t→∞ limits do not commute for entire classes of initial conditions. This is, for instance, the case for inertial planar rotators whenever...

Statistical mechanics can only be ultimately justified in terms of microscopic dynamics (classical, quantum, relativistic, or any other). It is known that Boltzmann–Gibbs statistics is based on the hypothesis of exponential sensitivity to the initial conditions, mixing and ergodicity in Gibbs...

The optimization of the recently generalized entropy of the form Sq ≡ 1 − ∝dx[p(x)]q∼/(q−1) with the constraints ∝dxp(x) = 1 and 〈x2〉q ≡ ∝dxx2[p(x)]q = 1 yields the Student's t-distribution for q > 1, and the r-distribution for q < 1.

We study a discrete N-component spin ferromagnet with Hamiltonian βH= −NK∑〈i,j〉(Si·Sj)−N2L∑〈i,j〉(Si·Sj)2 in a semi-infinite cubic lattice. The coupling constants at the surface, Ks and Ls, are allowed to be different from the bulk ones, KB and LB. Using a simple real-space...

We discuss the non-Boltzmannian nature of quasi-stationary states in the Hamiltonian mean field (HMF) model, a paradigmatic model for long-range interacting classical many-body systems. We present a theorem excluding the Boltzmann–Gibbs exponential weight in Gibbs Γ-space of microscopic...