Kappa Distributions; Kappa Distributions: Theory and Applications in Plasmas; Copyright; Contents; Contributors; Preface; 1 -- Theory and Formalism; 1 -- Statistical Background of Kappa Distributions: Connection With Nonextensive Statistical Mechanics; 1.1 Summary; 1.2 Introduction; 1.3 Mathematical Motivation; 1.4 Nonextensive Statistical Mechanics, in Brief!; 1.4.1 General Aspects; 1.4.2 q-Deformed Functions; 1.4.2.1 q-Unity; 1.4.2.2 q-Exponential; 1.4.2.3 q-Logarithm; 1.4.2.4 q-Hyperbolic; 1.4.2.5 q-Gamma; 1.4.3 Ordinary and Escort Probability Distributions; 1.4.4 Tsallis Entropy.
1.4.5 The Physical Temperature1.5 Entropy Maximization; 1.5.1 Discrete Description; 1.5.2 Continuous Description; 1.6 Connection of Kappa Distributions With Nonextensive Statistical Mechanics; 1.6.1 Derivation; 1.6.2 Historical Comments; 1.7 Structure of the Kappa Distribution; 1.7.1 The Base of the Kappa Distribution; 1.7.2 The Exponent of the Kappa Distribution; 1.8 The Concept of Temperature; 1.8.1 The Definition of Temperature Out of Equilibrium and the Concept of Physical Temperature; 1.8.2 Mean Kinetic Energy Defines Temperature; 1.8.3 Misleading Considerations About Temperature.
