Energy exchange in a bi-flux diffusion process consisting of particles of the same nature split into two distinct microstates

The present paper introduces a new approach to the dynamics of a particle system, split into two distinct microstates diffusing in a homogeneous medium. The particles belonging to the main microstate spread according to the classical Fick’s law and the complementary set moves excited by a new potential. Each set is associated with a particular energy level. The particles can move between the two sets, introducing a third flux which 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.