This note gives an account of a construction of an “elliptic quantum group” associated with each simple classical Lie algebra. It is closely related to elliptic face models of statistical mechanics, and, in its semiclassical limit, to the Wess-Zumino-Witten model of conformal field theory on tori. More details are presented in [Fe] and complete proofs will appear in a separate publication. Quan...

Through the H theorem, Bolzmann attempted to validate the foundations of statistical mechanics. However, it is incompatible with the fundamental laws of mechanics because its deduction requires the introduction of probability. In this paper we attempt a justification of statistical mechanics without deviating from the existing framework of quantum mechanics. We point out that the principle of e...

What is the physical significance of entropy? What is the physical origin of irreversibility? Do entropy and irreversibility exist only for complex and macroscopic systems? For everyday laboratory physics, the mathematical formalism of Statistical Mechanics (canonical and grand-canonical, Boltzmann, Bose-Einstein and Fermi-Dirac distributions) allows a successful description of the thermodynami...