Nonlinear Kinetics on Lattices based on the Kinetic Interaction Principle
arXiv:1806.00621 · 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.
arXiv comment26 pages
References in corpus (22)
- Non Linear Kinetics underlying Generalized Statistics
- Generalized thermodynamics and Fokker-Planck equations. Applications to stellar dynamics, two-dimensional turbulence and Jupiter's great red spot
- Deformed exponentials and logarithms in generalized thermostatistics
- Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations
- Group entropies, correlation laws and zeta functions
- Non-gaussian statistics and stellar rotational velocities of main sequence field stars
- Kinetical Foundations of Non Conventional Statistics
- Power-law statistics and stellar rotational velocities in the Pleiades
- Jeans instability criterion from the viewpoint of non-gaussian statistics
- Entropic Forms and Related Algebras
- The relativistic statistical theory and Kaniadakis entropy: an approach through a molecular chaos hypothesis
- Tsallis and Kaniadakis statistics from the viewpoint of entropic gravity formalism
- Canonical partition function for anomalous systems described by the -entropy
- Exploiting the flexibility of a family of models for taxation and redistribution
- A k-generalized statistical mechanics approach to income analysis
- A method to deconvolve stellar rotational velocities
- Composition law of -entropy for statistically independent systems
- k-Deformed Fourier Transform
- A k-deformed Model of Growing Complex Networks with Fitness
- Common Origin of Power-law Tails in Income Distributions and Relativistic Gases
- A discrete nonlinear mass transfer equation with applications in solid-state sintering of ceramic materials
- Kinetic Model of Mass Exchange with Dynamic Arrhenius Transition Rates