Related papers: Kinetic Entropy-Based Measures of Distribution Fun…
A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the…
We combine an axiomatics of R\'{e}nyi with the $q$--deformed version of Khinchin axioms to obtain a measure of information (i.e., entropy) which accounts both for systems with embedded self-similarity and non-extensivity. We show that the…
The purpose of the present effort is threefold. Firstly, it is shown that there exists a principle, that we call Kinetical Interaction Principle (KIP), underlying the non linear kinetics in particle systems, independently on the picture…
Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological, and social processes. The…
Context. Recent studies on Kappa distribution functions invoked in space plasma applications have emphasized two alternative approaches which may assume the temperature parameter either dependent or independent of the power-index $\kappa$.…
We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence of probability spaces and a sequence of measure-preserving maps between these spaces. This notion generalizes the classical concept of metric…
The science of thermodynamics was put together in the Nineteenth Century to describe large systems in equilibrium. One part of thermodynamics defines entropy for equilibrium systems and demands an ever-increasing entropy for non-equilibrium…
A novel nonlocal density functional for the kinetic pressure tensor of a Fermi gas is derived. The functional is designed to reconcile the Quantum Hydrodynamic Model with the microscopic approaches, both for homogeneous equilibrium and…
A novel route to instabilities and turbulence in fluid and plasma flows is presented in kinetic Vlasov-Maxwell model. New kind of flow instabilities is shown to arise due to the availability of new kinetic energy sources which are absent in…
Although density functional theory provides reliable predictions for the static properties of simple fluids under confinement, a theory of comparative accuracy for the transport coefficients has yet to emerge. Nonetheless, there is evidence…
The dispersion relation of longitudinal electrostatic oscillations in a relativistic plasma is studied in the context of the nonextensive statistics formalism proposed by Tsallis [C. Tsallis, J. Stat. Phys. {\bf 52}, 479 (1988)], where…
The plasma of quarks and gluons created in ultrarelativistic heavy-ion collisions turns out to be paramagnetic. In the presence of a background magnetic field, this paramagnetism thus leads to a pressure anisotropy, similar to anisotropies…
In this study, the physics of sheath formation in a collisional two-electron temperature plasma in the presence of an oblique external magnetic field has been investigated. At first, a comparative study among the fluid electron model,…
In plasmonics, nonlocal effects arise when the material response to optical excitations is strongly dependent on the spatial correlations of the excitation. It is well known that a classical free electron gas system supports local Drude…
We present a general and systematic theory of non-equilibrium dynamics of multi-component fluid membranes, in general, and membranes containing transmembrane proteins, in particular. Developed based on a minimal number of principles of…
We develop a purely hydrodynamic formalism to describe collisional, anisotropic instabilities in a relativistic plasma, that are usually described with kinetic theory tools. Our main motivation is the fact that coarse-grained models of high…
In space plasma, various effects of magnetic reconnection and turbulence cause the electron motion to significantly deviate from their Larmor orbits. Collectively these orbits affect the electron velocity distribution function and lead to…
In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme…
Distribution function is essential in statistical inference, and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates…
This article studies the asymptotic behaviors of nonparametric estimators of two overlapping measures, namely Pianka's and MacArthur-Levins measures. The plug-in principle and the method of kernel density estimation are used to estimate…