H-theorem for the (modified) nonlinear Enskog equation

Kinetic equation and nonequilibrium entropy for a quasi-two-dimensional gas

“…Equation (9) has some similarities with the one obtained in [21,22] in the context of the Enskog equation (for a non-confined fluid). The evolution equation for the confinement contribution to the entropy of the gas is derived by means of the continuity…”

“…The definition of H c (t) can be justified on the basis of a local equilibrium approximation for the general non-equilibrium N particle distribution function of the system [21,22], keeping only contributions up to the second virial coefficient. This corresponds to taking the pair correlation function of the system equal to unity, but keeping the finite size of the particles in the description of the collision term.…”

Aspects of Ergodic, Qualitative and Statistical Theory of Motion

“…absolutely continuous). Since Boltzmann's H-function is an example of such a function we shall call H-functions all such functions: among them one should also mention the "Resibois' H function" for systems described by Enskog's equation (hard sphere systems) and the "(Boltzmann) entropy" for systems in local thermal equilibrium [Re78], [GL03]. We recall that Boltzmann's H-function is defined by a coarse graining of phase space into "macrostates" determined by the occupation numbers f (p, q)d 3 pd 3 q of phase space cells d 3 pd 3 q around p, q and by defining…”

Boltzmann Entropy for Dense Fluids Not in Local Equilibrium

“…S(f t , E) should satisfy an H-theorem for general systems, including dense fluids. It was also noted there that the quantity shown by Resibois [9] to satisfy an H-theorem for f t evolving via the modified Enskog equation (expected to be accurate for moderately dense hard sphere gases) is in fact the Boltzmann entropy S(f t , E) for a system of hard spheres.…”