Related papers: q-Stirling's formula in Tsallis statistics
We present a study of both the ``Iterative Procedure'' and the ``$\beta \to \beta'$ transformation'', proposed by Tsallis et al (Physica A261, 534) to find the probabilities $p_i$ of a system to be in a state with energy $\epsilon_i$,…
The non-extensive canonical ensemble theory is reconsidered with the method of Lagrange multipliers by maximizing Tsallis entropy, with the constraint that the normalized term of Tsallis' $q-$average of physical quantities, the sum $\sum…
Tsallis' non-extensive entropy $S_q$ enables us to treat both a power and exponential evolutions of underlying microscopic dynamics on equal footing by adjusting the variable entropic index $q$ to proper one $q^*$. We propose an alternative…
Recent progresses in statistical mechanics indicate the Tsallis nonextensive thermostatistics as the natural generalization of the standard classical and quantum statistics, when memory effects and long-range forces are not negligible. In…
Statistical mechanics is generalized on the basis of an information theory for inexact or incomplete probability distributions. A parameterized normalization is proposed and leads to a nonextensive entropy. The resulting incomplete…
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
The statistical mechanics of a cloud of particles interacting via their gravitational potentials is an old problem which encounters some issues when the traditional Boltzmann-Gibbs statistics is applied. In this article, we consider the…
Based on Tsallis entropy and the corresponding deformed exponential function, generalized distribution functions for bosons and fermions have been used since a while. However, aiming at a non-extensive quantum statistics further…
Tsallis relative operator entropy was defined as a parametric extension of relative operator entropy and the generalized Shannon inequalities were shown in the previous paper. After the review of some fundamental properties of Tsallis…
It is shown that the Renyi entropy is as stable as the Tsallis entropy at least for Abe-Lesche counterexamples.
We apply non-extensive methods to the statistical analysis of fully developed turbulent flows. Probability density functions of velocity differences at distance r obtained by extremizing the Tsallis entropies coincide well with what is…
For non-equilibrium systems in a steady state we present two necessary and sufficient conditions for the emergence of $q$-canonical ensembles, also known as Tsallis statistics. These conditions are invariance requirements over the…
We define a general notion of entropy in elementary, algebraic terms. Based on that, weak forms of a scalar product and a distance measure are derived. We give basic properties of these quantities, generalize the Cauchy-Schwarz inequality,…
We use third constraint formulation of Tsallis statistics and derive the $q$-statistics generalization of non-equilibrium work relations such as the Jarzynski equality and the Crooks fluctuation theorem which relate the free energy…
The Stirling approximation formula for $n!$ dates from 1730. Here we give new and instructive proofs of this and related approximation formulae via tools of probability and statistics. There are connections to the Central Limit Theorem and…
We derive a scaling property from a fundamental nonlinear differential equation whose solution is the so-called q-exponential function. A scaling property has been believed to be given by a power function only, but actually more general…
Tsallis q-extension of statistics and fractal generalization of dynamics are two faces of the same physical reality, as well as the Kernel modern complexity theory. The fractal generalization dynamics is based at the multiscale -…
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…
For a dynamical system far from equilibrium, one has to deal with empirical probabilities defined through time-averages, and the main problem is then how to formulate an appropriate statistical thermodynamics. The common answer is that the…
We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential, or energy dissipation) on long time scales. Depending on the…