Here’s the fourth lecture from the Rotman Summer Institute on Foundations of Statistical Mechanics from July 14-20, 2013. Lots more to come.
In this lecture, Jos Uffink continues his earlier discussion of some of the prehistory of the kinetic theory of gases and statistical mechanics. First, Uffink discusses precursors to the kinetic theory of gases, including views from Boyle, Newton, and Bernoulli. He then briefly discusses the differences in state spaces between the kinetic theory of gases and statistical mechanics.
The second part of the lecture focuses on Boltzmann’s work in statistical mechanics. In particular, the roles played by the Stosszahlansatz and the ergodic hypothesis – assumptions about the physical behaviour of systems – are analyzed. Finally, Uffink talks about the relation between Boltzmann’s work and a formulation of the Second Law of thermodynamics, concluding that while Boltzmann extends the notion of entropy to non-equilibrium states thus broadening the scope of the Second Law, Boltzmann never considers adiabatic processes, which is narrower in scope than the original statement.
Thanks to Molly Kao for editing the video, and writing the above precis of the lecture.