Related papers: Maximal entropy distribution functions from genera…
A class of parametric distribution functions has been proposed in [C.DiTroia, Plasma Physics and Controlled Fusion,54,2012] as equilibrium distribution functions (EDFs) for charged particles in fusion plasmas, representing supra-thermal…
We consider a system of reaction-diffusion equations describing the reversible reaction of two species $\mathcal{U}, \mathcal{V}$ forming a third species $\mathcal{W}$ and vice versa according to mass action law kinetics with arbitrary…
Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing…
Based upon the rate equations for the photon distribution function obtained in the previous paper, we study the formal solutions in three different representation forms for the Sunyaev-Zeldovich effect. By expanding the formal solution in…
We analyze the entropy production in run-and-tumble models. After presenting the general formalism in the framework of the Fokker-Planck equations in one space dimension, we derive some known exact results in simple physical situations…
Particle distributions in weakly collisional environments such as the magnetosphere have been observed to show deviations from the Maxwellian distribution. These can often be reproduced in kinetic simulations, but fluid models, which are…
In a recent paper [Phys. Lett. A {\bf335}, 351 (2005)] the authors discussed the equivalence among the various probability distribution functions of a system in equilibrium in the Tsallis entropy framework. In the present letter we extend…
Maximum-entropy distributions are shown to appear in the probability calculus as approximations of a model by exchangeability or a model by sufficiency, the former model being preferable. The implications of this fact are discussed,…
Recent improvements in the method of estimating Renyi entropies from measurements of coincidences between the events observed in high energy collisions are reviewed. A new, more precise, formulation of the method is presented and its…
Shannon and Renyi entropies are quantitative measures of uncertainty in a data set. They are developed by Renyi in the context of entropy theory. These measures have been studied in the case of the multivariate t-distributions. We extend…
A run-and-tumble particle in a one dimensional box (infinite potential well) is studied. The steady state is analytically solved and analyzed, revealing the emergent length scale of the boundary layer where particles accumulate near the…
The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback--Leibler from the normal and half normal distributions are approximated using…
High-energy, multi-component plasmas in which pair creation and annihilation, lepton-lepton scattering, lepton-proton scattering, and Comptonization all contribute to establishing the particle and photon distributions, are present in a…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
Most astrophysical plasmas are observed to have velocity distribution functions exhibiting non-Maxwellian suprathermal tails. The high energy particle populations are accurately represented by the family of kappa-distributions where the use…
The generalization of the Zubarev nonequilibrium statistical operator method for the case of Renyi statistics is proposed when the relevant statistical operator (or distribution function) is obtained based on the principle of maximum for…
A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…
Renyi entropies S_q are useful measures of quantum entanglement; they can be calculated from traces of the reduced density matrix raised to power q, with q>=0. For (d+1)-dimensional conformal field theories, the Renyi entropies across…
The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized…
Conventional information-theoretic quantities assume access to probability distributions. Estimating such distributions is not trivial. Here, we consider function-based formulations of cross entropy that sidesteps this a priori estimation…