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We present a theory where the statistical mechanics for dilute ideal gasescan be derived from random matrix approach. We show the connection of thisapproach with Srednicki approach which connects Berry conjecture withstatistical mechanics. We further establish a link between Berry conjecture andrandom matrix theory, thus providing a unified edifice for quantum chaos,random matrix theory, and statistical mechanics. In the course of arguing forthese connections, we observe sum rules associated with the outstandingcounting problem in the theory of braid groups. We are able to show that thepresented approach leads to the second law of thermodynamics.Comment: 23 pages, TeX typ

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