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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
- Source :
- Entropy, Vol 25, Iss 10, p 1400 (2023)
- Publication Year :
- 2023
- Publisher :
- MDPI AG, 2023.
-
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.
Details
- Language :
- English
- ISSN :
- 10994300
- Volume :
- 25
- Issue :
- 10
- Database :
- Directory of Open Access Journals
- Journal :
- Entropy
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.f4829360ead54c14b8359b2c49e3b563
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/e25101400