Typicality in statistical mechanics and the arrow of time
Mathematical Challenges in Quantum Mechanics, online
January 10, 2024
In this lecture, I will give a brief overview of the foundations of statistical mechanics, with a focus on typicality in classical settings, and hint at generalizations to the quantum setting. This is a talk given in preparation for a presentation by H. Tasaki.
Slides
PDF:
LaTeX source:
 tarball: 24mcqm1.0.tar.gz
Further reading

S. Goldstein, J.L. Lebowitz, R. Tumulka, N. Zanghì  Gibbs and Boltzmann Entropy in Classical and Quantum Mechanics, Statistical Mechanics and Scientific Explanation, pp. 519581, 2020
doi:10.1142/9789811211720_0014, arXiv:1903.11870. 
S. Goldstein, D.A. Huse, J.L. Lebowitz, R. Tumulka  Macroscopic and microscopic thermal equilibrium, Annalen der Physik, volume 529, issue 7, number 1600301, 2017
doi:10.1002/andp.201600301, arXiv:1610.02312. 
H. Tasaki  Typicality of thermal equilibrium and thermalization in isolated macroscopic quantum systems, Journal of Statistical Physics, volume 163, pp. 937997, 2016
doi:10.1007/s1095501615112, arXiv:1507.06479. 
N. Shiraishi, H. Tasaki  Nature abhors a vacuum: A simple rigorous example of thermalization in an isolated macroscopic quantum system, 2023
arXiv:12310.18880.
Illustration of ergodicity
As an illustration of ergodicity and mixing, here is the Poincare section of two coupled pendula (see animations/coupledpendulum).