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.

Inferring Source Properties of Monoenergetic Electron Precipitation From Kappa and Maxwellian Moment-Voltage Relationships

We present two case studies of FAST electrostatic analyzer measurements of both highly nonthermal ( κ ≲  2.5) and weakly nonthermal/thermal monoenergetic electron precipitation at ∼4,000 km, from which we infer the properties of the magnetospheric source distributions via comparison of experimentally determined number density-, current density-, and energy flux-voltage relationships with corresponding theoretical relationships. We also discuss the properties of the two new theoretical number density-voltage relationships that we employ. Moment uncertainties, which are calculated analytically via application of the Gershman et al. (2015, https://doi.org/10.1002/2014JA020775) moment uncertainty framework, are used in Monte Carlo simulations to infer ranges of magnetospheric source population densities, temperatures, κ values, and altitudes. We identify the most likely ranges of source parameters by requiring that the range of κ values inferred from fitting experimental moment-voltage relationships correspond to the range of κ values inferred from directly fitting observed electron distributions with two-dimensional kappa distribution functions. Observations in the first case study, which are made over ∼78-79° invariant latitude in the Northern Hemisphere and 4.5-5.5 magnetic local time, are consistent with a magnetospheric source population density n m= 0.7-0.8 cm-3, source temperature T m≈ 70 eV, source altitude h= 6.4-7.7 R E, and κ= 2.2-2.8. Observations in the second case study, which are made over 76-79° invariant latitude in the Southern Hemisphere and ∼21 magnetic local time, are consistent with a magnetospheric source population density n m= 0.07-0.09 cm-3, source temperature T m≈ 95 eV, source altitude h ≳  6 R E, and κ= 2-6.

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.

Development and performance of a suprathermal electron spectrometer to study auroral precipitations

The design, development, and performance of Medium-energy Electron SPectrometer (MESP), dedicated to the in situ observation of suprathermal electrons in the auroral ionosphere, are summarized in this paper. MESP employs a permanent magnet filter with a light tight structure to select electrons with proper energies guided to the detectors. A combination of two avalanche photodiodes and a large area solid-state detector (SSD) provided 46 total energy bins (1 keV resolution for 3-20 keV range for APDs, and 7 keV resolution for >20 keV range for SSDs). Multi-channel ultra-low power application-specific integrated circuits are also verified for the flight operation to read-out and analyze the detector signals. MESP was launched from Poker Flat Research Range on 3 March 2014 as a part of ground-to-rocket electrodynamics-electrons correlative experiment (GREECE) mission. MESP successfully measured the precipitating electrons from 3 to 120 keV in 120-ms time resolution and characterized the features of suprathermal distributions associated with auroral arcs throughout the flight. The measured electrons were showing the inverted-V type spectra, consistent with the past measurements. In addition, investigations of the suprathermal electron population indicated the existence of the energetic non-thermal distribution corresponding to the brightest aurora.