Quantum Chaos, Random Matrix Theory, and Statistical Mechanics in Two Dimensions - A Unified Approach

We present a theory where the statistical mechanics for dilute ideal gases can be derived from random matrix approach. We show the connection of this approach with Srednicki approach which connects Berry conjecture with statistical mechanics. We further establish a link between Berry conjecture and random matrix theory, thus providing a unified edifice for quantum chaos, random matrix theory and statistical mechanics. 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. PACS numbers:05.30.-d 05.45.+b Typeset using REVTEX 1