Related papers: Maximal entropy distribution functions from genera…
We find the value of constants related to constraints in characterization of some known statistical distributions and then we proceed to use the idea behind maximum entropy principle to derive generalized version of this distributions using…
The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…
We consider the Student-t and Student-r distributions, which maximise Renyi entropy under a covariance condition. We show that they have information-theoretic properties which mirror those of the Gaussian distributions, which maximise…
Computing the stochastic entropy production associated with the evolution of a stochastic dynamical system is a well-established problem. In a small number of cases such as the Ornstein-Uhlenbeck process, of which we give a complete…
We introduce a new set of generalized Fokker-Planck equations that conserve energy and mass and increase a generalized entropy until a maximum entropy state is reached. The concept of generalized entropies is rigorously justified for…
We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we…
The Renyi entropy is a generalisation of the Shannon entropy that is sensitive to the fine details of a probability distribution. We present results for the Renyi entropy of the totally asymmetric exclusion process (TASEP). We calculate…
Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the non-equilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary…
This paper is devoted to $\phi$-entropies applied to Fokker-Planck and kinetic Fokker-Planck equations in the whole space, with confinement. The so-called $\phi$-entropies are Lyapunov functionals which typically interpolate between Gibbs…
We study the convergence analysis for general degenerate and non-reversible stochastic differential equations (SDEs). We apply the Lyapunov method to analyze the Fokker-Planck equation, in which the Lyapunov functional is chosen as a…
In previous works, we derived stationary density distribution functions (DDF) where the local equilibrium is determined by imposing the maximum entropy (MaxEnt) principle, under the scale invariance restrictions, and the minimum entropy…
One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker-Planck equation in $\mathbb R^d$ with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear…
In this study an attempt has been made to propose a way to develop new distribution. For this purpose, we need only idea about distribution function. Some important statistical properties of the new distribution like moments, cumulants,…
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…
It is possible to derive the maximum entropy principle from thermodynamic stability requirements. Using as a starting point the equilibrium probability distribution, currently used in non-extensive thermostatistics, it turns out that the…
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…
In this paper we derive the maximum entropy characteristics of a particular rank order distribution, namely the discrete generalized beta distribution, which has recently been observed to be extremely useful in modelling many several…
The momentum entropic moments and R\'enyi entropies of a one-dimensional particle in an infinite well potential are found by means of explicit calculations of some Dirichlet-like trigonometric integrals. The associated spreading lengths and…
Relative entropy is a fundamental class of distances between probability distributions, with widespread applications in probability theory, statistics, and machine learning. In this work, we study relative entropy from a categorical…
The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…