Related papers: Non Linear Kinetics underlying Generalized Statist…
We provide a detailed multiscale analysis of a system of particles interacting through a dynamical network of links. Starting from a microscopic model, via the mean field limit, we formally derive coupled kinetic equations for the particle…
We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under…
While linear systems are well-understood, no explicit solution for general nonlinear systems exists. A classical approach to make the understanding of linear system available in the nonlinear setting is to represent a nonlinear system by a…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
Recently Mazenko and Das and Mazenko introduced a non-equilibrium field theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
The thermodynamics and covariant kinetic theory have been elaborately investigated in a non-extensive environment considering the non-extensive generalization of Bose-Einstein (BE) and Fermi-Dirac (FD) statistics. Starting with Tsallis'…
The gap in statistics between multi-variate and time-series analysis can be bridged by using entropy statistics and recent developments in multi-dimensional scaling. For explaining the evolution of the sciences as non-linear dynamics, the…
We study a nonlinear recombination model from population genetics as a combinatorial version of the Kac-Boltzmann equation from kinetic theory. Following Kac's approach, the nonlinear model is approximated by a mean field linear evolution…
We investigate kinetic entropy-based measures of the non-Maxwellianity of distribution functions in plasmas, i.e., entropy-based measures of the departure of a local distribution function from an associated Maxwellian distribution function…
The main purpose of this article is to guide the reader to theorems on global properties of solutions to the Einstein-Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important…
Conjecture II.3.6 of Spohn in [Spohn '91] and Lecture 7 of Jensen-Yau in [Jensen-Yau '99] ask for a general derivation of universal fluctuations of hydrodynamic limits in large-scale stochastic interacting particle systems. However, the…
In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…
An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point articles placed in $\mathbb{R}^d (d \geq 1)$. The particles perform random jumps with pair wise repulsion, in the…
We develop a method using a coarse graining of the energy fluctuations of an equilibrium quantum system which produces simple parameterizations for the behaviour of the system. As an application, we use these methods to gain more…
For deterministic continuous time nonlinear control systems, epsilon-practical stabilization entropy and practical stabilization entropy are introduced. Here the rate of attraction is specified by a KL-function. Upper and lower bounds for…
We introduce the concept of kinetic equations representing a natural extension of the more conventional notion of a kinetic relation. Algebraic kinetic relations, widely used to model dynamics of dislocations, cracks and phase boundaries,…
A wide range of non-equilibrium phenomena in nature involve non-reciprocal interactions. To understand the novel behaviors that can emerge in such systems, finding tractable models is essential. With this goal, we introduce a non-reciprocal…
The nonextensive kinetic theory for degenerate quantum gases is discussed in the general relativistic framework. By incorporating nonadditive modifications in the collisional term of the relativistic Boltzmann equation and entropy current,…
A reformulation of quantum mechanics called ``hybrid interaction picture'' (HIP) is proposed. In contrast to its current non-Hermitian-interaction-picture (NIP) predecessor the new formalism combines a simplification of the NIP…