Quasi-Conformality of a Non-Extensive Entropy and Kappa Distributions

Abstract:

The Havrda-Charvat/Daroczy/Cressie-Read/Tsallis entropy has attracted substantial attention in the Physics

literature during the last 25 years. It is intimately related to the kappa distributions that are of great interest

in Plasma Physics. One of the most important questions in these investigations is the

microscopic origin and ab initio determination of the kappa/non-extensive parameter that appears in these distributions.

To determine its origin, it may be beneficial to explore some of the formal properties of the underlying entropic functional.

Initial numerical, and mostly circumstantial, evidence points toward symmetries of the kappa parameter exhibited by systems

described by this kappa ("Tsallis") entropy. Such symmetries are reminiscent of the conformal symmetries which are present in

numerous cases of Physical interest such as second order phase transitions. In this exposition, we explore the origin of this

conjectured symmetry of the kappa/non-extensive parameter.

Our treatment relies in an essential way on the (quasi-) conformal properties of the kappa/Tsallis entropic functional and its

related equilibrium kappa/q-exponential distributions.