Diffusion laws, information and action principle

We study diffusion phenomena from the point of view of information theory. The system of interest with a given Hamiltonian is placed in the context of stochastic dynamics. According to the result of our recent work, this dynamic system maximizes its uncertainty of motion measured by a path information in order to follow the least action principle of mechanics. In this work, this methodology is applied to particle diffusion in external potential field. Thanks to the exponential probability distribution of action (least action distribution) given by maximum path information, a general derivation of Fokker-Planck equation, Fick’s laws and Ohm’s law for normal diffusion is given without additional assumptions about the nature of the process (Brownian and Markovian or not). This result is a proof of the physical robustness of the least action distribution and strongly suggests that, for irregular dynamics, the method of maximum path information, instead of the principle of least action for regular dynamics, should be used in order to obtain the correct occurring probability of different paths of transport. The limits of validity of this this work is discussed. PACS numbers : 02.50.Ey (Stochastic processes); 05.45.-a (Nonlinear dynamics); 66.10.Cb (Diffusion)