相关论文: New Class of Generalized Extensive Entropies for S…
The asymptotic convergence of probability density function (pdf) and convergence of differential entropy are examined for the non-stationary processes that follow the maximum entropy principle (MaxEnt) and maximum entropy production…
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…
The principle of maximum entropy (Maxent) is often used to obtain prior probability distributions as a method to obtain a Gibbs measure under some restriction giving the probability that a system will be in a certain state compared to the…
We describe a maximum entropy approach for computing volumes and counting integer points in polyhedra. To estimate the number of points from a particular set X in R^n in a polyhedron P in R^n, by solving a certain entropy maximization…
The R\'enyi entropy is a generalization of the Shannon entropy and is widely used in mathematical statistics and applied sciences for quantifying the uncertainty in a probability distribution. We consider estimation of the quadratic R\'enyi…
We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint…
We present simple and computationally efficient nonparametric estimators of R\'enyi entropy and mutual information based on an i.i.d. sample drawn from an unknown, absolutely continuous distribution over $\R^d$. The estimators are…
It is shown that R\'enyi statistics provides a plausible basis to describe the hadron distributions measured in high energy particle interactions. Generalized Boltzmann and gamma distributions obtained by maximization of R\'enyi entropy…
We construct the complete set of orders of growth and we define on it the generalized entropy of a dynamical systems. With this object we provide a framework where we can study the separation of orbits of a map beyond the scope of…
The R\'enyi entropies $R_{p}[\rho]$, $p>0,\neq 1$ of the highly-excited quantum states of the $D$-dimensional isotropic harmonic oscillator are analytically determined by use of the strong asymptotics of the orthogonal polynomials which…
Generalized entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information…
Pesin's formula relates the entropy of a dynamical system with its positive Lyapunov exponents. It is well known, that this formula holds true for random dynamical systems on a compact Riemannian manifold with invariant probability measure…
Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the R\'enyi entropies is expected to enhance their scope in…
We propose R\'enyi information generating function and discuss its properties. A connection between the R\'enyi information generating function and the diversity index is proposed for discrete type random variables. The relation between the…
With the help of a general expression of the entropies in extensive and nonextensive systems, some important relations between thermodynamics and statistical mechanics are revealed through the views of thermodynamics and statistic physics.…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…
A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for…
The kinetic theory of gases provides methods for calculating Lyapunov exponents and other quantities, such as Kolmogorov-Sinai entropies, that characterize the chaotic behavior of hard-ball gases. Here we illustrate the use of these methods…
From the analyticity properties of the equation governing infinitesimal perturbations, it is shown that all stability properties of spatially extended 1D systems can be derived from a single function that we call entropy potential since it…
We show how quasiprobability distribution functions defined over $N^{2}$-dimensional discrete phase spaces can be used to treat physical systems described by a finite space of states which exhibit spin tunneling effects. This particular…