Related papers: Relativity, nonextensivity, and extended power law…
In this paper, we obtain the law of emergence with Tsallis entropy from the thermodynamic laws. We first derive the law of emergence from the equilibrium description of the unified first law and Clausius relation. However, it has been shown…
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 analysis of high-energy particle collisions is an excellent testbed for the non-extensive statistical approach. In these reactions we are far from the thermodynamical limit. In small colliding systems, such as electron-positron or…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
The nonextensivity in a non-isothermal plasma system with the Coulombian long-range interactions is studied in the framework of Tsallis statistics. We present for first time a mathematical expression of the nonextensive parameter q based on…
To reveal how nonequilibrium physics and relativity theory intertwine, this articles studies relativistic Brownian motion under cosmic expansion. Two fluctuation theorems for the entropy ds, which is locally produced in this extreme…
It is shown that the distribution derived from the principle of maximum Tsallis entropy is a superposable Levy-type distribution. Concomitantly, the leading order correction to the limit distribution is also deduced. This demonstration…
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…
Tsallis' non-extensive entropy is extended to incorporate the dependence on affinities between the microstates of a system. At the core of our construction of the extended entropy ($\mathcal{H}$) is the concept of the effective number of…
Two important problems existing in Tsallis' statistics are investigated, where one is whether energy is extensive or not, and the other is whether it is necessary to introduce the so-called generalized zeroth law of thermodynamics or not.…
We briefly review Boltzmann-Gibbs and nonextensive statistical mechanics as well as their connections with Fokker-Planck equations and with existing central limit theorems. We then provide some hints that might pave the road to the proof of…
Kullback-Leibler relative-entropy has unique properties in cases involving distributions resulting from relative-entropy minimization. Tsallis relative-entropy is a one parameter generalization of Kullback-Leibler relative-entropy in the…
A mapping of nonextensive statistical mechanics into Gibbs' statistical mechanics exists, which leads to a generalization of Einstein's formula for fluctuations. A unified treatment of stability of relaxed states in nonextensive statistical…
The cornerstone of Boltzmann-Gibbs ($BG$) statistical mechanics is the Boltzmann-Gibbs-Jaynes-Shannon entropy $S_{BG} \equiv -k\int dx f(x)\ln f(x)$, where $k$ is a positive constant and $f(x)$ a probability density function. This theory…
The asymptotic correspondence between the probability mass function of the $q$-deformed multinomial distribution and the $q$-generalised Kullback-Leibler divergence, also known as Tsallis relative entropy, is established. The probability…
The low-temperature form of the equilibrium relativistic mass distribution is subject to the Galilean limit by taking $c\rightarrow \infty .$ In this limit the relativistic Maxwell-Boltzmann distribution passes to the usual nonrelativistic…
It is well known that the particular form of the two-particle correlation function, in the collisional integral of the classical Boltzmman equation, fix univocally the entropy of the system, which turn out to be the Boltzmann-Gibbs-Shannon…
The nonextensive statistics based on the $q$-entropy $S_q=-\frac{\sum_{i=1}^v(p_i-p_i^q)}{1-q}$ has been so far applied to systems in which the $q$ value is uniformly distributed. For the systems containing different $q$'s, the…
We generalize the second law of thermodynamics in its maximum work formulation for a nonequilibrium initial distribution. It is found that in an isothermal process, the Boltzmann relative entropy (H-function) is not just a Lyapunov function…
Nonadditive Tsallis $q$-statistics has successfully been applied for a plethora of systems in natural sciences and other branches of knowledge. Nevertheless, its foundations have been severely criticised by some authors based on the…