  3. Note that Boltzmann misconstrues, or perhaps understates, the significance of his results. Both the Boltzmann equation and the H theorem refer to a body of gas in a fixed container that evolves in complete isolation from its environment. There is no question of heat being exchanged by the gas during a process, let alone in an irreversible cyclic process. His comparison with Clausius' integral \(\int dQ/T\) (i.e., \(\oint \dbar Q/T\) in modern notation) is therefore really completely out of place.