Game theoretic simulations and entropy dynamics framework for modeling complex material interactions

Abstract

Molecular dynamics is a technique used to understand how the interactions between atoms control complex material behavior under internal and external forces. We use a game theoretical approach to simulate molecular interactions, build material surrogates, and study material nature as a function of the Coulomb potential. The electric Coulomb potential is applicable in studying electromagnetic properties, for instance, electrical conductivity and dielectric permittivity. We investigate how probability densities of material positions and charges influence the diffusion process induced by this potential. By exploiting the information hidden in the seemingly random molecular exchanges, we show that an information-theoretical measure of entropy can describe the dynamics of material interactions. In particular, we use the Renyi entropy to derive posterior density representing the most likely particle distribution after these exchanges and thus connect molecular dynamics to entropy dynamics.