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- W4309136131 abstract "The Boltzmann distribution is commonly interpreted as a classical approximation of the quantum-mechanical Fermi-Dirac and Bose-Einstein distributions. We arrive at a different conclusion by directly investigating the three equilibrium distributions without considering statistical variations. A general differential equation of thermal equilibrium is obtained that applies to any particles. Simple integration yields the Boltzmann distribution. Furthermore, quantum conditions are established, ruling the occupation numbers of (i) fermions by utilizing Pauli's exclusion principle and (ii) bosons by utilizing Einstein's rate-equation approach to Planck's law of blackbody radiation. By exploiting the respective quantum condition, integration of the same differential equation of thermal equilibrium yields either the Fermi-Dirac or the Bose-Einstein distribution. It suggests that the Boltzmann distribution is a general distribution of thermal equilibrium, whereas the Fermi-Dirac and Bose-Einstein distributions are special cases of the Boltzmann distribution, ruled by specific conditions. This suggestion is further underlined by the fact that inserting the respective quantum condition directly into the Boltzmann distribution delivers either the Fermi-Dirac or the Bose-Einstein distribution. This finding implies that fermions and bosons simultaneously obey both their own specific and the general Boltzmann distribution." @default.
- W4309136131 created "2022-11-23" @default.
- W4309136131 creator A5031372095 @default.
- W4309136131 date "2022-11-10" @default.
- W4309136131 modified "2023-09-23" @default.
- W4309136131 title "Differential Equation of Thermal Equilibrium, Quantum Conditions, and Relation between Boltzmann, Fermi-Dirac, and Bose-Einstein Distributions" @default.
- W4309136131 doi "https://doi.org/10.48550/arxiv.2211.07401" @default.
- W4309136131 hasPublicationYear "2022" @default.
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