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.