Boltzmann's H-theorem and kinetic equations

We discuss the celebrated H-theorem of Boltzmann and its ramifications in the Boltzmann and Landau equations. Time permitting, we outline a proof of the H-theorem's validity in spatially homogeneous equations. We will also introduce entropy's arch-nemesis—dispersion—in the spatially inhomogeneous case. Finally, we will give some conjectures and open questions that abound in the field.