Abstract
Classical and quantum Gibbs ensembles are constructed for equilibrium statistical mechanics in the framework of an extension to many-body theory of a relativistic mechanics proposed by Stueckelberg. In addition to the usual chemical potential in the grand canonical ensemble, there is a new potential corresponding to the mass degree of freedom of relativistic systems. It is shown that in the nonrelativistic limit the relativistic ensembles we have obtained reduce to the usual ones, and mass fluctuations for the free-particle gas approach the fluctuations in N. The ultrarelativistic limit of the canonical ensemble for the free-particle gas differs from the corresponding limit of the ensemble proposed by Jüttner and Pauli. Due to the mass degree of freedom, the quantum counting of states is different from that of the nonrelativistic theory. If the mass distribution is sufficiently sharp, the thermodynamical effects of this multiplicity will not be large. There may, however, be detectable effects such as a shift in the Fermi level and the critical temperature for Bose-Einstein condensation, and some change in specific heats.
| Original language | English |
|---|---|
| Pages (from-to) | 306-340 |
| Number of pages | 35 |
| Journal | Annals of Physics |
| Volume | 137 |
| Issue number | 2 |
| DOIs | |
| State | Published - Dec 1981 |
| Externally published | Yes |
Bibliographical note
Funding Information:* A preliminary version of this work was published in “Proceedings, 13th IUPAP Conference on Statistical Physics, Technion, Haifa, Israel, 1977” (C. Weil, D. Cabib, C. G. Kuper, and Ban Riess, Eds.), Annals of the Israel Physical Society, Vol. 2, p. 924 Adam Hilger, Bristol, 1978. This paper was presented by W. C. Schieve at STATPHYS 14, Edmonton, August, 1980. ‘Research supported in part by the U. S.-Israel Binational Science Foundation Israel.
Funding
* A preliminary version of this work was published in “Proceedings, 13th IUPAP Conference on Statistical Physics, Technion, Haifa, Israel, 1977” (C. Weil, D. Cabib, C. G. Kuper, and Ban Riess, Eds.), Annals of the Israel Physical Society, Vol. 2, p. 924 Adam Hilger, Bristol, 1978. This paper was presented by W. C. Schieve at STATPHYS 14, Edmonton, August, 1980. ‘Research supported in part by the U. S.-Israel Binational Science Foundation Israel.
| Funders | Funder number |
|---|---|
| United States-Israel Binational Science Foundation |