Related papers: Conservative Force Fields in Non-Gaussian Statisti…
We derive the hydrodynamic limit of a kinetic equation where the interactions in velocity are modelled by a linear operator (Fokker-Planck or Linear Boltzmann) and the force in the Vlasov term is a stochastic process with high amplitude and…
We derive the pressure tensor and the heat flux to accompany the new macroscopic conservation equations that we developed previously in a volume-based kinetic framework for gas flows. This kinetic description allows for expansion or…
We apply a variant of the Nose-Hoover thermostat to derive the Hamiltonian of a nonextensive system that is compatible with the canonical ensemble of the generalized thermostatistics of Tsallis. This microdynamical approach provides a…
The statistical mechanical partition function can be used to construct different forms of phase space distributions not restricted to the Gibbs-Boltzmann factor. With a generalised Lorentzian both the Kappa-Bose and Kappa-Fermi partition…
This work formulates and gives grounds for general principles and theorems that question the energy function doctrine and its quantum version as a genuine law of nature without borders of adequacy. The emphasis is on the domain where the…
Proper modeling of complex systems requires innovative mathematical tools. In this sense, we sought to use deformed or fractal derivatives for studying the dynamics of systems, particularly those, such as granular gases, in which the…
We show that the general two-variable Langevin equations with inhomogeneous noise and friction can generate many different forms of power-law distributions. By solving the corresponding stationary Fokker-Planck equation, we can obtain a…
Recent studies have outlined the interest for the evaluation of transport coefficients in space plasmas, where the observed velocity distributions of plasma particles are conditioned not only by the binary collisions, e.g., at low energies,…
We apply kinetic field theory to non-linear cosmic structure formation. Kinetic field theory decomposes the cosmic density field into particles and follows their trajectories through phase space. We assume that initial particle momenta are…
The existence of a weak solution to a McKean-Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under natural conditions. The distribution of any solution to the…
We discuss the use of Kaniadakis' $\kappa$-exponential in the construction of a statistical manifold modelled on Lebesgue spaces of real random variables. Some algebraic features of the deformed exponential models are considered. A chart is…
We show that in weakly confining conservative force fields, a subclass of diffusion-type (Smoluchowski) processes, admits a family of "heavy-tailed" non-Gaussian equilibrium probability density functions (pdfs), with none or a finite number…
A mechanism is proposed for the appearance of power law distributions in various complex systems. It is shown that in a conservative mechanical system composed of subsystems with different numbers of degrees of freedom a robust power-law…
The propagation of ion acoustic shocks in nonthermal plasmas is investigated, both analytically and numerically. An unmagnetized collisionless electron-ion plasma is considered, featuring a superthermal (non-Maxwellian) electron…
We introduce a variant of the replica trick within the nonlinear sigma model that allows calculating the distribution function of the persistent current. In the diffusive regime, a Gaussian distribution is derived. This result holds in the…
A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the…
We introduce a fractional Kramers equation for a particle interacting with a thermal heat bath and external non-linear force field. For the force free case the velocity damping follows the Mittag-Leffler relaxation and the diffusion is…
The energy loss pattern of a low momentum heavy quark in a deconfined quark-gluon plasma can be understood in terms of a Langevin description. In thermal equilibrium, the motion can then be parametrized in terms of a single heavy quark…
The Hawkes self-excited point process provides an efficient representation of the bursty intermittent dynamics of many physical, biological, geological and economic systems. By expressing the probability for the next event per unit time…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…