Nonextensive Statistical Mechanics: Equivalence Between Dual Entropy and Dual Probabilities

The concept of duality of probability distributions constitutes a fundamental “brick” in the solid framework of nonextensive statistical mechanics—the generalization of Boltzmann–Gibbs statistical mechanics under the consideration of the q-entropy. The probability duality is solving old-standing issues of the theory, e.g., it ascertains the additivity for the internal energy given the additivity in the energy of microstates. However, it is a rather complex part of the theory, and certainly, it cannot be trivially explained along the Gibb’s path of entropy maximization. Recently, it was shown that an alternative picture exists, considering a dual entropy, instead of a dual probability. In particular, the framework of nonextensive statistical mechanics can be equivalently developed using q- and 1/q- entropies. The canonical probability distribution coincides again with the known q-exponential distribution, but without the necessity of the duality of ordinary-escort probabilities. Furthermore, it is shown that the dual entropies, q-entropy and 1/q-entropy, as well as, the 1-entropy, are involved in an identity, useful in theoretical development and applications.

Kappa Distributions: Statistical Physics and Thermodynamics of Space and Astrophysical Plasmas

Kappa distributions received impetus as they provide efficient modelling of the observed particle distributions in space and astrophysical plasmas throughout the heliosphere. This paper presents (i) the connection of kappa distributions with statistical mechanics, by maximizing the associated q-entropy under the constraints of the canonical ensemble within the framework of continuous description; (ii) the derivation of q-entropy from first principles that characterize space plasmas, the additivity of energy, and entropy; and (iii) the derivation of the characteristic first order differential equation, whose solution is the kappa distribution function.

Evidence for global electron transportation into the jovian inner magnetosphere

Jupiter's magnetosphere is a strong particle accelerator that contains ultrarelativistic electrons in its inner part. They are thought to be accelerated by whistler-mode waves excited by anisotropic hot electrons (>10 kiloelectron volts) injected from the outer magnetosphere. However, electron transportation in the inner magnetosphere is not well understood. By analyzing the extreme ultraviolet line emission from the inner magnetosphere, we show evidence for global inward transport of flux tubes containing hot plasma. High-spectral-resolution scanning observations of the Io plasma torus in the inner magnetosphere enable us to generate radial profiles of the hot electron fraction. It gradually decreases with decreasing radial distance, despite the short collisional time scale that should thermalize them rapidly. This indicates a fast and continuous resupply of hot electrons responsible for exciting the whistler-mode waves.