Ludwig Boltzmann made tremendously important contributions to the problem of connecting\ macroscopic, empirical phenomena with microscopic, atomistic dynamics. At the end\ of the nineteenth century, Boltzmann was confronted with various strong objections to his\ work. For example, Boltzmann\textquoterights atomistic explanations presuppose the reality of atoms, a\ notion that was vigorously rejected in some circles [14, 38]. Then too, there was the critique\ by Loschmidt that Boltzmann\textquoterights H-theorem, put forth as a microscopic explanation for the\ Second Law of Thermodynamics, could hardly account for irreversible physics when the individual\ two-atom collisions were each reversible [18, 42]. Still intriguing today is the existence\ of special cases of the Boltzmann equation in which time-varying distributions of atoms resist\ the imperative of equilibration, even in the presence of collisions. Boltzmann discussed\ such situations in a paper dedicated to responding to Loschmidt\textquoterights critique [7, 4]. Perhaps\ Boltzmann\textquoterights motivation was to enumerate special cases where his famous H value does not\ relax as it should, and by enumerating them, point out their nonnaturalness, their artificiality.\ Damping, or relaxation to equilibrium, of a time-invariant phase-space distribution, is\ an all-but universal result predicted by the Boltzmann equation.

}, year = {2015}, volume = {Ph. D.}, pages = {139}, month = {07-2015}, publisher = {University of Colorado Boulder}, address = {Boulder, CO}, }