Related papers: Entropies based on fractional calculus
Chater and MacKay [CM] derived an entropy function of state for exchange economies satisfying a list of axioms, and showed that a change of state of a system of such economies is possible if and only if their total entropy does not…
The Shannon-Khinchin axioms are generalized to nonextensive systems and the uniqueness theorem for the nonextensive entropy is proved rigorously. In the present axioms, Shannon additivity is used as additivity in contrast to…
We present aspects of entropic functionals relatively recently introduced in Physics which are non-additive, in the conventional sense of the word, some of which have a power-law functional form. We use as an example among them, and to be…
Entropy conservation and stability of numerical methods in gas dynamics have received much interest. Entropy conservative numerical fluxes can be used as ingredients in two kinds of schemes: Firstly, as building blocks in the subcell flux…
The definitions of the temperature in the nonextensive statistical thermodynamics based on Tsallis entropy are analyzed. A definition of pressure is proposed for nonadditive systems by using a nonadditive effective volume. The…
We show that the thermal subadditivity of entropy provides a common basis to derive a strong form of the bounded difference inequality and related results as well as more recent inequalities applicable to convex Lipschitz functions, random…
We discuss the properties of invariant measures corresponding to iterated function systems (IFSs) with place-dependent probabilities and compute their Renyi entropies, generalized dimensions, and multifractal spectra. It is shown that with…
The Shannon-Khinchin axioms for the ordinary information entropy are generalized in a natural way to the nonextensive systems based on the concept of nonextensive conditional entropy, and a complete proof of the uniqueness theorem for the…
This article extends the non-extensive entropy of Tsallis and uses this entropy to model an energy producing system in an absorbing heat bath. This modified non-extensive entropy is superficially identical to the one proposed by Tsallis,…
Entropy-conservative numerical flux functions can be used to construct high-order, entropy-stable discretizations of the Euler and Navier-Stokes equations. The purpose of this short communication is to present a novel family of such…
We deploy Shannon's information entropy to the distribution of branching fractions in a particle decay. This serves to quantify how important a given new reported decay channel is, from the point of view of the information that it adds to…
Entropy functions played a key role in the development of mathematical theory for hyperbolic conservation laws. The notion of entropy, which is intimately connected with symmetry, is an extension \emph{imposed} on nonlinear systems of…
With use of the Second Inverse Maximum Entropy Principle we find entropy functions for systems with fractal distribution functions with order parameter $q$. We compare these entropy functions with those given by the Bose-Einstein and…
Entropy functionals are computed for non-stationary distributions of particles of Lorentz gas and hard disks. The distributions consisting of beams of particles are found to have the largest amount of entropy and entropy increase. The…
Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with…
We shall show that a two-parameter extended entropy function is characterized by a functional equation. As a corollary of this result, we obtain that the Tsallis entropy function is characterized by a functional equation, which is a…
We consider two types of entropy, namely, Shannon and R\'{e}nyi entropies of the Poisson distribution, and establish their properties as the functions of intensity parameter. More precisely, we prove that both entropies increase with…
In this paper, we give a review of fractal calculus which is an expansion of standard calculus. Fractal calculus is applied for functions which are not differentiable or integrable on totally disconnected fractal sets such as middle-$\mu$…
Landauer's Principle relates entropy decrease and heat dissipation during logically irreversible processes. Most theoretical justifications of Landauer's Principle either use thermodynamic reasoning or rely on specific models based on…
The aim of this work is to analyze the entropy, entropy flux and entropy supply rate of granular fluids within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas…