Diffusion and memory effect in a stochastic process and the correspondence to an information propagation in a social system

Abstract

A generalized Langevin equation is suggested to describe a diffusion particle system with memory. The equation can be transformed into the Fokker–Planck equation by using the Kramers–Moyal expansion. The solution of Fokker–Planck equation can describe not only the diffusion of particles but also that of opinion particles based on the similarities between the two. We find that the memory can restrain some non-equilibrium phenomena of velocity distribution in the system, without memory, induced by correlation between the noise and space (Wang et al., 2021). However, the memory can enhance the effective collision among particles as shown by the variation of diffusion coefficients, and changes the diffusion mode between the dissipative and pumping region by comparing with that in the aforementioned system without memory. As the discussions in this physical system is paralleled to a social system, the random diffusion of social ideology, such as the information propagation, can be suppressed by the correlation between the noise and space.