Preprint Article Version 1 This version is not peer-reviewed

Nonlinear Kinetics on a Lattice Featuring Anomalous Diffusion

Version 1 : Received: 30 April 2018 / Approved: 2 May 2018 / Online: 2 May 2018 (11:36:35 CEST)

A peer-reviewed article of this Preprint also exists.

Kaniadakis, G.; Hristopulos, D.T. Nonlinear Kinetics on Lattices Based on the Kinetic Interaction Principle. Entropy 2018, 20, 426. Kaniadakis, G.; Hristopulos, D.T. Nonlinear Kinetics on Lattices Based on the Kinetic Interaction Principle. Entropy 2018, 20, 426.

Journal reference: Entropy 2018, 20, 426
DOI: 10.3390/e20060426

Abstract

Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker-Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker-Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker-Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker-Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP) that governs the particle kinetics of many body systems, introduced in [G. Kaniadakis, Physica A 296, 405 (2001)], univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker-Planck equation in its most general form.

Subject Areas

Fokker-Planck equations; fermion statistics; boson statistics; Haldane statistics; Kinetic interaction principle; anomalous diffusion; Fokker-Planck current

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.