Abstract
The concept of entropy is central, not only for the thermodynamics of equilibrium systems but also for non-equilibrium systems. Therefore, it is of interest to discuss the entropy for Kappa distributions. Related to a theoretical foundation for the standard Kappa distributions the extensitivity of entropy has been questioned for plasma systems that are described with constituents exhibiting power-law velocity distributions. While a related debate about the consequences of non-extensive entropy is still ongoing, it has been demonstrated that the regularized Kappa distributions, which have been introduced in order to remove several conceptual difficulties accompanying standard Kappa distributions, are consistent with an extensive entropy. So, by way of a regularization, Kappa distributions are made consistent with the laws of standard thermodynamics. We review here the different entropy concepts for Kappa distributions and illustrate them quantitatively in comparison to the Maxwellian case.
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References
R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics (1975)
R. Balescu, Transport Processes in Plasmas (North-Holland, Amsterdam, 1988)
L. Boltzmann, Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen: Vorgelegt in der Sitzung am 10 October 1872 (k. und k. Hof- und Staatsdruckerei, 1872).
J.C. Brown, G. Beekman, N. Gray, A.L. MacKinnon, Astron. Astrophys. 299, 629 (1995)
C. Cercignani, Kinetic Theory and Gas Dynamics (1988)
H. Fichtner, K. Scherer, M. Lazar, H.J. Fahr, Z. Vörös, Phys. Rev. E. 98(5), 053205 (2018). https://doi.org/10.1103/PhysRevE.98.053205
J. Gibbs, Elementary Principles in Statistical Mechanics: Developed with Especial Reference to the Rational Foundations of Thermodynamics. Elementary Principles in Statistical Mechanics: Developed with Especial Reference to the Rational Foundation of Thermodynamics (C. Scribner’s sons, New York, 1902).
K. Goeke, Statistik und Thermodynamik (2010). https://doi.org/10.1007/978-3-8348-9748-0
W. Grandy, Entropy and the Time Evolution of Macroscopic Systems. International Series of Monographs on Physics (OUP, Oxford, 2008)
S. Kullback, R.A. Leibler, Ann. Math. Statist. 22(1), 79 (1951). https://doi.org/10.1214/aoms/1177729694
M. Lingam, L. Comisso, Phys. Plasmas 25(1), 012114 (2018). https://doi.org/10.1063/1.5020887
Y.E. Litvinenko, Astrophys. J. 880(1), 20 (2019). https://doi.org/10.3847/1538-4357/ab2760
M. Nauenberg, Phys. Rev. E 67(3), 036114 (2003). https://doi.org/10.1103/PhysRevE.67.036114
M. Nauenberg, Phys. Rev. E 69(3), 038102 (2004). https://doi.org/10.1103/PhysRevE.69.038102
A.R. Plastino, H.G. Miller, A. Plastino, Phys. Rev. E 56(4), 3927 (1997). https://doi.org/10.1103/PhysRevE.56.3927
K. Scherer, H. Fichtner, M. Lazar, EPL (Europhys. Lett.) 120(5), 50002 (2017). https://doi.org/10.1209/0295-5075/120/50002
K. Scherer, M. Lazar, E. Husidic, H. Fichtner, Astrophys. J. 880(2), 118 (2019). https://doi.org/10.3847/1538-4357/ab1ea1
K. Scherer, E. Husidic, M. Lazar, H. Fichtner, Mon. Not. Roy. Astron. Soc. 497(2), 1738 (2020). https://doi.org/10.1093/mnras/staa1969
K. Scherer, E. Husidic, M. Lazar, H. Fichtner, Mon. Not. Roy. Astron. Soc. 501(1), 606 (2021). https://doi.org/10.1093/mnras/staa3641
B.D. Shizgal, Astrophys. Space Sci. 312(3–4), 227 (2007). https://doi.org/10.1007/s10509-007-9679-1
J. Silva, R., A.R. Plastino, J.A.S. Lima, Phys. Lett. A 249(5–6), 401 (1998). https://doi.org/10.1016/S0375-9601(98)00710-5
R.A. Treumann, W. Baumjohann, Front. Phys. 8, 221 (2020). https://doi.org/10.3389/fphy.2020.00221.
C. Tsallis, J. Stat. Phys. 52, 479 (1988). https://doi.org/10.1007/BF01016429
C. Tsallis, Phys. Rev. E 69(3), 038101 (2004). https://doi.org/10.1103/PhysRevE.69.038101
C. Tsallis, D.J. Bukman, Phys. Rev. E 54(3), R2197 (1996). https://doi.org/10.1103/PhysRevE.54.R2197
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Fichtner, H., Scherer, K., Lazar, M., Fahr, HJ., Vörös, Z. (2021). Kappa Distributions and Entropy. In: Lazar, M., Fichtner, H. (eds) Kappa Distributions. Astrophysics and Space Science Library, vol 464. Springer, Cham. https://doi.org/10.1007/978-3-030-82623-9_14
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DOI: https://doi.org/10.1007/978-3-030-82623-9_14
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