Related papers: Generalized Fractional Statistics
We studied multiple quantum harmonic oscillators in the Tsallis statistics of entropic parameter $q$ in the cases that the distributions are power-like, separately applying the conventional expectation value, the unnormalized…
It is shown how, among a class of generalized entropies, the Tsallis entropy can uniquely be identified by the principles of thermodynamics, the concept of stability and the axiomatic foundation.
A generalized-statistics variational principle for source separation is formulated by recourse to Tsallis' entropy subjected to the additive duality and employing constraints described by normal averages. The variational principle is…
It is shown that Tsallis' generalized statistics provides a natural frame for the statistical-thermodynamical description of anomalous diffusion. Within this generalized theory, a maximum-entropy formalism makes it possible to derive a…
We give a formulation of the single particle occupation probabilities for a system of identical particles obeying fractional exclusion statistics of Haldane. We first derive a set of constraints using an exactly solvable model which…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
Extensions of Fannes' inequality with partial sums of the Tsallis entropy are obtained for both the classical and quantum cases. The definition of kth partial sum under the prescribed order of terms is given. Basic properties of introduced…
Generalized entropy, that has been recently proposed, puts all the known and apparently different entropies like The Tsallis, the R\'{e}nyi, the Barrow, the Kaniadakis, the Sharma-Mittal and the loop quantum gravity entropy within a single…
We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on…
The necessary information for specifying a complex system may not be completely accessible to us, i.e., to mathematical treatments. This is not to be confounded with the incompleteness of our knowledge about whatever systems or nature,…
We study a version of the generalized (h, {\phi})-entropies, introduced by Salicr\'u et al, for a wide family of probabilistic models that includes quantum and classical statistical theories as particular cases. We extend previous works by…
We consider the self-similar phase space with reduced fractal dimension $d$ being distributed within domain $0<d<1$ with spectrum $f(d)$. Related thermostatistics is shown to be governed by the Tsallis' formalism of the non-extensive…
A definition of the nonadditive (nonextensive) conditional entropy indexed by q is presented. Based on the composition law in terms of it, the Shannon-Khinchin axioms are generalized and the uniqueness theorem is established for the Tsallis…
We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of…
The origin of non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Recent results indicate a connection between non-extensive statistics and thermofractals. After reviewing this connection, we…
We first show how a new definition of entropy, which is intuitively very simple, as a divergence in cluster-size space, leads to a generalized form that is nonextensive for correlated units, but coincides exactly with the conventional one…
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum…
The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized…
In a recent paper, Phys. Rev. Lett. 105 260601 (2010) [arXiv:1008.1421], Andrade et al., argued that classical particles confined in a parabolic trap at T=0 distribute themselves in accordance with the Tsallis statistics. To prove their…
We show that starting with either the non-extensive Tsallis entropy in Wang's formalism or the extensive Renyi entropy, it is possible to construct the equilibrium statistical mechanics with non-Gibbs canonical distribution functions. The…