Inverse relationship between diffusion coefficient and mass for a free particle system: Approach by using maximum caliber principle and Monte Carlo simulations

Abstract

A derivation of the diffusion equation is presented using the maximum caliber principle and the continuity equation for a system composed of paths traveled by a free particle in a time interval. By identifying the diffusion coefficient in the obtained diffusion equation, it is shown that there is an inverse proportionality relationship concerning the particle’s mass so that a higher mass is related to lower diffusion, and the lower mass is connected to the higher diffusion. This relationship is also shown using Monte Carlo simulations to sample the path space for a free particle system and then using the time slicing equation to obtain the probability of the particle position for each time showing the diffusion behavior for different masses.