On the thermal relaxation of a dense gas described by the modified Enskog equation in a closed system in contact with a heat bath

The thermal relaxation of a dense gas described by the modified Enskog equation is studied for a closed system in contact with a heat bath. As in the case of the Boltzmann equation, the Helmholtz free energy $\mathcal{F}$ that decreases monotonically in time is found under the conventional kinetic boundary condition that satisfies the Darrozes–Guiraud inequality. The extension to the modified Enskog–Vlasov equation is also presented.