2001-09-26
10:15 at ML J 21

Duality between thermodynamics and kinetics in Tsallis nonextensive statistical mechanics

Iliya Karlin

Institute of Polymers, ETH Zentrum

I'm going to discuss the properties of the Tsallis' q-deformations of thermodynamics and kinetics. Deformation of the Boltzmann kinetic equation is considered as an example for the latter. It is demonstrated that the use of q-deformed macroscopic variables (such as energy and momentum) required in Tsallis' approach to thermodynamics, results in a duality, that is, the set of thermodynamic equilibria this way obtained cannot be a result of the q-deformed kinetics, and vice versa, the set of stationary states of the q-deformed kinetics cannot be the q-deformed thermodynamic equilibria, all this except for q=1 (Boltzmann's entropy). Rather, these sets are related by a duality transform of the deformation parameter q, and which is explicitly obtained. Implications of this duality will be discussed.