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Title
Japanese: 
English:Reconsideration of Temperature Determined by the Excited-State Population Distribution of Hydrogen Atoms Based on Tsallis Entropy and Its Statistics in Hydrogen Plasma in Non-Equilibrium State 
Author
Japanese: 菊池浩司, 赤塚洋.  
English: Koji Kikuchi, Hiroshi Akatsuka.  
Language English 
Journal/Book name
Japanese: 
English:Entropy 
Volume, Number, Page Vol. 25    Issue 10    p. 1400
Published date Sept. 29, 2023 
Publisher
Japanese: 
English:MDPI 
Conference name
Japanese: 
English: 
Conference site
Japanese: 
English: 
Official URL https://www.mdpi.com/1099-4300/25/10/1400
 
DOI https://doi.org/10.3390/e25101400
Abstract In non-equilibrium plasmas, the temperature cannot be uniquely determined unless the energy-distribution function is approximated as a Maxwell–Boltzmann distribution. To overcome this problem, we applied Tsallis statistics to determine the temperature with respect to the excited-state populations in non-equilibrium state hydrogen plasma, which enables the description of its entropy that obeys q-exponential population distribution in the non-equilibrium state. However, it is quite difficult to apply the q-exponential distribution because it is a self-consistent function that cannot be solved analytically. In this study, a self-consistent iterative scheme was adopted to calculate q-exponential distribution using the similar algorithm of the Hartree–Fock method. Results show that the excited-state population distribution based on Tsallis statistics well captures the non-equilibrium characteristics in the high-energy region, which is far from the equilibrium-Boltzmann distribution. The temperature was calculated using the partial derivative of entropy with respect to the mean energy based on Tsallis statistics and using the coefficient of q-exponential distribution. An analytical expression was derived and compared with Boltzmann statistics, and the distribution was discussed from the viewpoint of statistical physics.

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