(Last updated: 11/03/2024)

Additional Notes / Extra Content

• Introduction to Thermodynamics
  • This set of notes is a pretty thorough interpolation of the story told to me when I was an undergraduate studying thermodynamics for the first time. I aim to aid that discussion here, providing some formal treatment to the notions introduced in class. (This document is being continuously updated as questions and comments come in.)
• The Three Ensembles
  • In this chapter, we explore the basic ideas of statistical mechanics and how to construct the various statistical ensembles that commonly arise in tackling problems. I start with some ideas from Hamiltonian mechanics and use Boltzmann’s postulate to construct the microcanonical ensemble, before demonstrating how the canonical and grand canonical ensembles are obtained under suitable couplings to reservoirs.
• Quantum Gases
  • Now, we turn our attention to the study of the Bose and Fermi gases. Specifically, I introduce the basic ideas necessary to understand why the grand canonical ensemble is most suitable, then dive into more detailed studies of the two gases with some useful computations involving the polylogarithm formalism.
• (In Progress) The Thermodynamics of Computation