On the thermodynamics of volume/mass diffusion in fluids
  In Physica A vol 387(24) (2008) pp6079-6094 [1], a kinetic equation for gas flows was proposed that leads to a set of four macroscopic conservation equations, rather than the traditional set of three equations. The additional equation arises due to local spatial random molecular behavior, which has been described as a volume or mass diffusion process. In this present paper, we describe a procedure to construct a Gibbs-type equation and a second-law associated with these kinetic and continuum models. We also point out the close link between the kinetic equation in [1] and that proposed previously by Klimontovich, and we discuss some of their compatibilities with classical mechanical principles. Finally, a dimensional analysis highlights the nature of volume/mass diffusion: it is a non-conventional diffusive process, with some similarities to the `ghost effect', which cannot be obtained from a fluid mechanical derivation that neglects non-local-equilibrium structures, as the conventional Navier-Stokes-Fourier model does. 
S. Kokou Dadzie and Jason M. Reese
math-ph math.MP