  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.
