Related papers: New exponential, logarithm and q-probability in th…
Entropy maximization procedure has been a general practice in many diverse fields of science to obtain the concomitant probability distributions. The consistent use of the maximization procedure on the other hand requires the probability…
This paper follows recent steps towards a nonassociative quantum theory and points out the mathematical structure behind the proposed modifications to conventional quantum theory. An N=1 supersymmetry model and a strong force glueball…
In this didactical note I review in depth the rationale for using generalised canonical distributions in quantum statistics. Particular attention is paid to the proper definitions of quantum entropy and quantum relative entropy, as well as…
We look at multiparticle production processes from the nonextensive point of view. Nonextensivity means here the systematic deviations in exponential formulas provided by the usual statistical approach for description of some observables…
Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or…
The translated logarithmic Lambert function is defined and basic analytic properties of the function are obtained including the derivative, integral, Taylor series expansion, real branches and asymptotic approximation of the function.…
The non-extensive statistical mechanics has been used to describe a variety of complex systems. The maximization of entropy, often used to introduce the non-extensive statistical mechanics, is a formal procedure and does not easily leads to…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
We formulate a convenient generalization of the q-expectation value, based on the analogy of the symmetric quantum groups and q-calculus, and show that the q->q^{-1} symmetric nonextensive entropy preserves all of the mathematical structure…
Increasing the number $N$ of elements of a system typically makes the entropy to increase. The question arises on {\it what particular entropic form} we have in mind and {\it how it increases} with $N$. Thermodynamically speaking it makes…
Probability distributions defined on the half space are known to be quite different from those in the full space. Here, a nonextensive entropic treatment is presented for the half space in an analytic and self-consistent way. In this…
In ths paper we discuss the new concept of the q-extension of Genocchi numbers and give the some relations between q-Genocchi polynomials and q-Euler numbers.
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence…
New formulations of quantum generalized fluctuation-dissipation relations in terms of characteristic and probabilistic functionals of continuous observations are suggested and discussed. It is shown that control of entropy production in…
The log-periodic equation for the entropy $S = - (k/a) \sum_{i=1}^{N} p_{i} \sin(a \ln p_{i})$, based on the forgotten Sharma-Taneja entropy measure, is studied for the first time with $N$ the total number of system states and $p_{i}$ the…
For noncommutative variables x,y an expansion of log(exp(x)exp(y)) in powers of x+y is obtained.Each term of the series is given by an infinite sum in powers of x-y.The series is represented by diagrams.
Exponential family distributions are highly useful in machine learning since their calculation can be performed efficiently through natural parameters. The exponential family has recently been extended to the t-exponential family, which…
We consider the joint density distribution of the elements of certain random matrix models which are example of globally correlated and asymptotically scale-invariant distributions. It is shown that in their cases, the nonadditive entropy…
In a recent letter (EPL, 104 (2013) 60003) we suggested a way to avoid divergences inherent to the formulation of nonextensive statistical mechanics. They can be eliminated via the use of a q-Laplace transformation, which was illustrated…