Related papers: Generalizing the Planck distribution
We develop the argument that the Gibbs-von Neumann entropy is the appropriate statistical mechanical generalisation of the thermodynamic entropy, for macroscopic and microscopic systems, whether in thermal equilibrium or not, as a…
Power-law distributions are widely observed in complex systems, yet establishing their thermodynamic consistency remains a theoretical challenge. In this paper, we present a thermodynamic framework for power-law statistics based on the…
In the process of analyzing the axiomatic principles underlying statistical physics, when modeling the most probable stationary macrostates of non-ergodic closed systems, a forecast was obtained about a possible limitation purview of the…
It has been advanced, on experimental (P.-M. Robitaille, IEEE Trans. Plasma Sci. 2003, v. 31(6), 1263-1267) and theoretical (P.M. Robitaille, Progr. Phys. 2006, v.2, 22-23) grounds, that blackbody radiation is not universal and remains…
We study the effects, to all orders in the Planck length from a generalized uncertainty principle (GUP), on the statistical entropy of massive scalar bulk fields in the Randall-Sundrum black brane world. We show that the Bekenstein-Hawking…
This article studies the breaking of the Lorentz symmetry at the Planck length in quantum mechanics. We use three-dimensional p-adic vectors as position variables, while the time remains a real number. In this setting, the Planck length is…
We generalize Einstein's master equation for random walk processes by considering that the probability for a particle at position $r$ to make a jump of length $j$ lattice sites, $P_j(r)$ is a functional of the particle distribution function…
Based on quantum statistical mechanics and microscopic quantum dynamics, we prove Planck's and Kelvin's principles for macroscopic systems in a general and realistic setting. We consider a hybrid quantum system that consists of the…
Thermodynamical quantities of the blackbody radiation, such as free energy, entropy, total radiation energy, specific heat are calculated within the Tsallis thermostatistics where factorization method is incorparated. It is shown that basic…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
We formulate a short-time expansion for one-dimensional Fokker-Planck equations with spatially dependent diffusion coefficients, derived from stochastic processes with Gaussian white noise, for general values of the discretization parameter…
We numerically study a one-dimensional system of $N$ classical localized planar rotators coupled through interactions which decay with distance as $1/r^\alpha$ ($\alpha \ge 0$). The approach is a first principle one (\textit{i.e.}, based on…
We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with…
We consider asymptotic normality of linear rank statistics under various randomization rules met in clinical trials and designed for patients' allocation into treatment and placebo arms. Exposition relies on some general limit theorem due…
A Langevin equation is suggested to describe a system driven by correlated Gaussian white noise as well as with positive and negative damping demarcated by a critical velocity. The equation can be transformed into the Fokker-Planck equation…
The use of statistical methods for the description of complex quantum systems was primarily motivated by the failure of a line-by-line interpretation of atomic spectra. Such methods reveal regularities and trends in the distributions of…
We consider a previously proposed non-extensive statistical mechanics in which the entropy depends only on the probability, this was obtained from a f(\beta) distribution and its corresponding Boltzmann factor. We show that the first term…
We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial…
A variety of phenomena in nuclear and high energy physics seemingly do not satisfy the basic hypothesis for possible stationary states to be of the type covered by Boltzmann-Gibbs (BG) statistical mechanics. More specifically, the system…
We consider a measure $\psi$ k of dispersion which extends the notion of Wilk's generalised variance, or entropy, for a d-dimensional distribution, and is based on the mean squared volume of simplices of dimension k $\le$ d formed by k + 1…