Related papers: The q-exponential family in statistical physics
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…
In this paper, the particles of quantum gases, that is, bosons and fermions are regarded as g-ons which obey fractional exclusion statistics. With this point of departure the thermostatistical relations concerning the Bose and Fermi systems…
The original canonical ensemble formalism for the nonextensive entropy thermostatistics is reconsidered. It is shown that the unambiguous connection of the statistical mechanics with the equilibrium thermodynamics is provided if the…
The paper demonstrates that the canonical probability distribution of the occupancy numbers of a bosonic system is multinomial, and shows how the thermodynamics of the canonical system descends from this distribution. The categorical…
Boltzmann-Gibbs statistical mechanics applies satisfactorily to a plethora of systems. It fails however for complex systems generically involving strong space-time entanglement. Its generalization based on nonadditive $q$-entropies…
The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the…
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…
We combine an axiomatics of R\'{e}nyi with the $q$--deformed version of Khinchin axioms to obtain a measure of information (i.e., entropy) which accounts both for systems with embedded self-similarity and non-extensivity. We show that the…
Topp-Leone distribution is a continuous model distribution used for modelling lifetime phenomena. The main purpose of this paper is to introduce a new framework for generating lifetime distributions, called the Topp-Leone generated…
An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q-1 (entropic nonextensivity) as a simple and efficient manner to…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…
We consider the wide class of few-particle systems that have some analog of the thermodynamic laws. These systems are characterized by the distributions that are determined by the Hamiltonian and satisfy the Liouville equation. Few-particle…
We study four distinct families of Gibbs canonical distributions defined on the standard complex, quaternionic, real and classical (nonquantum) two-level systems. The structure function or density of states for any two-level system is a…
The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the…
The most complicated phenomena of equilibrium statistics, phase separations and transitions of various order and critical phenomena, can clearly and sharply be seen even for small systems in the topology of the curvature of the…
Gibbs and Boltzmann definitions of temperature agree only in the macroscopic limit. The ambiguity in identifying the equilibrium temperature of a finite sized `small' system exchanging energy with a bath is usually understood as a…
We develop a method using a coarse graining of the energy fluctuations of an equilibrium quantum system which produces simple parameterizations for the behaviour of the system. As an application, we use these methods to gain more…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the N-body phase space with the given total energy. Due to Boltzmann's principle,…
Exponential families comprise a broad class of statistical models and parametric families like normal distributions, binomial distributions, gamma distributions or exponential distributions. Thereby the formal representation of its…
Traditionally, it is understood that fluctuations in the equilibrium distribution are not evident in thermodynamic systems of large $N$ (the number of particles in the system) \cite{Huang1}. In this paper we examine the validity of this…