Quantum chaos, random matrix theory, statistical mechanics in two dimensions, and the second law - A case study

We present a theory where the statistical mechanics for dilute ideal gases can be derived from the random matrix approach. We show the connection of this approach with the Srednicki approach which connects Berry conjecture with statistical mechanics. We further establish a link between Berry conjecture and random matrix theory. In the course of arguing for these connections, we also observe sum rules associated with the outstanding counting problem in the theory of Braid groups. We believe that these arguments, developed for a special example connecting the properties of eigenfunctions and random matrices to the second law of thermodynamics, will eventually prove co be more general.