Related papers: Microscopic interpretation of generalized entropy
The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation…
We give several inequalities on generalized entropies involving Tsallis entropies, using some inequalities obtained by improvements of Young's inequality. We also give a generalized Han's inequality.
In many applications, the probability density function is subject to experimental errors. In this work the continuos dependence of a class of generalized entropies on the experimental errors is studied. This class includes the C. Shannon,…
A new method is proposed for a treatment of ideal quantum gases in the microcanonical ensemble near the thermodynamic limit. The method allows rigorous asymptotic calculations of the average number of particles and particle number…
The most efficient MC weights for the calculation of physical, canonical expectation values are not necessarily those of the canonical ensemble. The use of suitably generalized ensembles can lead to a much faster convergence of the…
Microcanonical equations for several thermodynamic properties of a system, suitable for molecular dynamics simulations, are derived from the nonextensive Tsallis entropy functional. Two possible definitions of temperature, the usual one and…
We have discussed the Tsallis entropy in finite $N$-unit nonextensive systems, by using the multivariate $q$-Gaussian probability distribution functions (PDFs) derived by the maximum entropy methods with the normal average and the…
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is 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…
We revisit the cut-off prescriptions which are needed in order to specify completely the form of Tsallis' maximum entropy distributions. For values of the Tsallis entropic parameter $q>1$ we advance an alternative cut-off prescription and…
Thermalization (generalized thermalization) in nonintegrable (integrable) quantum systems requires two ingredients: equilibration and agreement with the predictions of the Gibbs (generalized Gibbs) ensemble. We prove that observables that…
The pathway model of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure. This entropy is a variant of the generalized entropy of order 'alpha', considered in Mathai and Rathie (1975), and…
In a previous paper, we introduced an axiomatic system for information thermodynamics, deriving an entropy function that includes both thermodynamic and information components. From this function we derived an entropic probability…
Thermodynamics and its quantum counterpart are traditionally described with statistical ensembles. Canonical typicality has related statistical mechanics for a system to ensembles of global energy eigen- states of system and its environment…
Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizes a fundamental limitation of operations by the second law of thermodynamics. The entropy is also expressed as the Shannon…
In a paper [8] the authors classify entropy into three categories, as a thermodynamics quantity, as a measure of information production, and as a means of statistical inference. An entropy measure introduced by Mathai falls into the second…
Systems with a long-term stationary state that possess as a spatio-temporally fluctuation quantity $\beta$ can be described by a superposition of several statistics, a "super statistics". We consider first, the Gamma, log-normal and…
The pathway model of Mathai (2005) mainly deals with the rectangular matrix-variate case. In this paper the scalar version is shown to be associated with a large number of probability models used in physics. Different families of densities…
Devising a statistical mechanics framework for jammed granular materials is a challenging task as those systems do not share some important properties required to characterize them with statistical thermodynamics tools. In a recent paper…
The paper deals with the generalization of both Boltzmann entropy and distribution in the light of most-probable interpretation of statistical equilibrium. The statistical analysis of the generalized entropy and distribution leads to some…