Related papers: q-Exponential Structure of Arbitrary-Order Reactio…
A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…
We discuss a Tsallis distribution with complex nonextensivity parameter $q$. In this case the usual distribution is decorated with a log-periodic oscillating factor (apparently, such oscillations can bee seen in recently measured transverse…
The incomplete nonextensive statistics in the canonical and microcanonical ensembles is explored in the general case and in a particular case for the ideal gas. By exact analytical results for the ideal gas it is shown that taking the…
Modeling of process for reaction kinetics is a fashionable subject of publications. The meaning of both the mortality and fertility terms are mathematically analyzed in details involving variation of their power exponents. We developed an…
We derived the expression of the normalized $q$-expectation value based on the density operator to the order $1-q$ with the physical temperature in the Tsallis nonextensive statistics of entropic parameter $q$. With the derived expression…
We show that the function beta(E) derived from the density of states of a constant heat capacity reservoir coupled to some system of interest is not identical to the physically measurable (transitive) temperature. There are, however,…
A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise…
A kinetic chemotaxis model with attractive interaction by quasistationary chemical signalling is considered. The special choice of the turning operator, with velocity jumps biased towards the chemical concentration gradient, permits closed…
The concept of reaction extent (the progress of a reaction, advancement of the reaction, conversion, etc.) was introduced around 100 years ago. Most of the literature provides a definition for the exceptional case of a single reaction step…
Starting from second order around thermal equilibrium, the response of a statistical mechanical system to an external stimulus is not only governed by dissipation and depends explicitly on dynamical details of the system. The so called…
In many situations, in all branches of physics, one encounters power-like behavior of some variables which are best described by a Tsallis distribution characterized by a nonextensivity parameter $q$ and scale parameter $T$. However, there…
The Boltzmann-Gibbs probability distribution, seen as a statistical model, belongs to the exponential family. Recently, the latter concept has been generalized. The q-exponential family has been shown to be relevant for the statistical…
Some results for the black-body radiation obtained in the context of the $q$-thermostatistics are analyzed on both thermodynamical and statistical-mechanical levels. Since the thermodynamic potentials can be expressed in terms of the…
The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation…
The nonextensive one-dimensional version of a hydrodynamical model for multiparticle production processes is proposed and discussed. It is based on nonextensive statistics assumed in the form proposed by Tsallis and characterized by a…
The nonextensive entropic measure proposed by Tsallis introduces a parameter, q, which is not defined but rather must be determined. The value of q is typically determined from a piece of data and then fixed over the range of interest. On…
We give an approach to exponential stability within the framework of evolutionary equations due to [R. Picard. A structural observation for linear material laws in classical mathematical physics. Math. Methods Appl. Sci.,…
A time-dependent statistical description of multiple particle breakage is presented. The approach combines the Tsallis non-extensive entropy with a fractal kinetic equation for the time variation of the number of fragments. The obtained…
Multispecies reaction-diffusion systems, for which the time evolution equation of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time…
A two-parameter deformation of the Touchard polynomials, based on the NEXT $q$-exponential function of Tsallis, defines two statistics on set partitions. The generating function of classical Touchard polynomials is a composition of two…