HTheorem for the (Modified) Nonlinear Enskog Equation

I construct an entropy function $S\left(t\right)\mathrm{}$ suitable for a system of hard spheres satisfying the (modified) nonlinear Enskog equation, and show that ${\partial }_{t}S\left(t\right)\mathrm{}>~0$. The equality sign holds only when the system has reached absolute equilibrium, in which case $S$ becomes the exact equilibrium entropy of the hard-sphere fluid.