Energy exchange in a dual flow diffusion process that consists of particles of the same nature divided into two different microstates

Abstract: This article presents a new approach to the dynamics of a particle system, divided into two distinct microstates spreading out in a homogeneous medium. The particles belonging to the main microstate spread according to classical Fick's law and the complementary set moves excitedly by a new potential. Each set is associated with a certain energy level. The particles can move between the two sets, introducing a third flow that is internal to the system. The governing equation is a fourth order PDE containing two new parameters, which can be time-dependent functions, in addition to the classical diffusion constant. It is shown that the solutions can avoid violations of the mass conservation requirements.