Related papers: Entropy functions and functional equations
It has been recently argued, via very clever arguments, that the MaxEnt variational problem would not adequately work for Renyi's and Tsallis' entropies. We constructively show here that this is not so if one formulates the associated…
In this paper I will discuss the overlap between the concept of Shannon Entropy and the concept of electronic correlation. Quantum Monte Carlo numerical results for the uniform electron gas are also presented; these latter on the one hand…
We consider a family of probability distributions depending on a real parameter and including the binomial, Poisson and negative binomial distributions. The corresponding index of coincidence satisfies a Heun differential equation and is a…
The uniqueness theorem for Tsallis entropy was presented in {\it H.Suyari, IEEE Trans. Inform. Theory, Vol.50, pp.1783-1787 (2004)} by introducing the generalized Shannon-Khinchin's axiom. In the present paper, this result is generalized…
We establish a general class of entropy inequalities that take the concise form of Gaussian comparisons. The main result unifies many classical and recent results, including the Shannon-Stam inequality, the Brunn-Minkowski inequality, the…
We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the…
Algorithmic entropy and Shannon entropy are two conceptually different information measures, as the former is based on size of programs and the later in probability distributions. However, it is known that, for any recursive probability…
Plastino, Rocca and Pennini [Phys. Rev. E \textbf{94} (2016) 012145] recently stated that the R\'enyi entropy is not suitable for thermodynamics by using functional calculus, since it leads to anomalous results unlike the Tsallis entropy.…
The connection between Tsallis entropy for a multifractal distribution and Jackson's $q$-derivative is established. Based on this derivation and definition of a homogeneous function, a $q$-analogue of Shannon's entropy is discussed.…
The increased uncertainty and complexity of nonlinear systems have motivated investigators to consider generalized approaches to defining an entropy function. New insights are achieved by defining the average uncertainty in the probability…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…
The Shannon entropy, the desequilibrium and their generalizations (R\'enyi and Tsallis entropies) of the three-dimensional single-particle systems in a spherically-symmetric potential $V(r)$ can be decomposed into angular and radial parts.…
It is shown that the standard expression for the information entropy, originally due to Shannon, is only valid for a particular set of states. For the general case of statistical mechanics, one needs to include an additional term in the…
Entropy is the measure of uncertainty in any data and is adopted for maximisation of mutual information in many remote sensing operations. The availability of wide entropy variations motivated us for an investigation over the suitability…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
This paper connects two methods for finding the functional of entropy in F(R)-Gravity: Padmanabhan's and Hammad's. The resulting approach is simple to follow and yields entropy functional, which can be separated into two parts. The part…
We show that Abe's general pseudoadditivity for entropy prescribed by thermal equilibrium in nonextensive systems holds not only for entropy, but also for energy. The application of this general pseudoadditivity to Tsallis entropy tells us…
The entropy of a closure operator has been recently proposed for the study of network coding and secret sharing. In this paper, we study closure operators in relation to their entropy. We first introduce four different kinds of rank…
An amended MaxEnt formulation for systems displaced from the conventional MaxEnt equilibrium is proposed. This formulation involves the minimization of the Kullback-Leibler divergence to a reference $Q$ (or maximization of Shannon…