MARKOV PROCESSES AND DISPERSION THEORY
Adrian E. Scheidegger · International Association of Scientific Hydrology Bulletin · 1965
It is shown that the forward Kolmogorov equation, as applied to dispersion processes, can be deduced as a special case from general non-equilibrium statistical mechanics in which there is a non-negative constant of the motion. For Markov processes, this constant can be taken as the integral over the whole system of the joint-probability density, and hence a master equation, identical to the forward Kolmogorov equation, follows for the latter.