THEORY OF KAPPA DISTRIBUTIONS AND NONEXTENSIVE STATISTICAL MECHANICS: APPLICATIONS IN ASTROPHYSICAL PLASMAS
Classical collisional particle systems residing in thermal equilibrium have their particle velocity/energy distribution function stabilized into a Maxwell Boltzmann distribution. On the contrary, space and astrophysical plasmas are exotic collisionless particle systems residing in stationary states characterized by the so called kappa distributions [1 3] A breakthrough in the field came with the connection of kappa distributions with statistical mechanics and thermodynamics, accomplished by the following two findings: (i) kappa distributions maximize the entropy of nonextensive statistical mechanics [4] under the constraints of canonical ensemble [5 8] and (ii) particle systems exchanging heat with each other reaching thermodynamic equilibrium are stabilized always into a kappa distribution [9,10] Thereafter, kappa distributions became increasingly widespread across the physics of astrophysical plasma processes, describing particles in the heliosphere, from the solar wind and planetary magnetospheres to the heliosheath and beyond, the interstellar and intergalactic plasmas [1] The lecture will review the physical foundations and recent developments of kappa distributions in space and astrophysical plasmas. References: [1] G. Livadiotis: Kappa distributions: Theory and applications in plasmas, (Elsevier, Netherlands, UK, USA, 2017) [2] V. Pierrard and M. Lazar: Kappa distributions: theory and applications in space plasmas, Sol. Phys. 267, 153 174 (2010) [3] G. Livadiotis and D.J. McComas: Understanding kappa distributions: A toolbox for space science and astrophysics, Space Sci. Rev. 75, 183 214 (2013) [4] C. Tsallis: Introduction to nonextensive statistical mechanics, (Springer, New York, 2009) [5] R.A. Treumann: Theory of superdiffusion for the magnetopause, Geophys. Res. Lett. 24, 17271730 (1997) [6] A.V. Milovanov and L.M. Zelenyi: Functional background of the Tsallis entropy: "coarse grained" systems and "kappa" distribution functions, Nonlin. Processes Geophys. 7, 211 221 (2000) [7] M.P. Leubner: A nonextensive entropy approach to kappa distributions, Astrophys. Space Sci. 282, 573 579 (2002) [8] G. Livadiotis and D.J. McComas: Beyond kappa distributions: Exploiting Tsallis statistical mechanics in space plasmas, J. Geophys. Res. 114, A11105 (2009) [9] S. Abe: General pseudoadditivity of composable entropy prescribed by the existence of equilibrium, Phys. Rev. E, 63, 061105 (2001) [10] G. Livadiotis: Thermodynamic origin of kappa distributions, Europhys. Lett. 122, 50001 (2018)