Classical statistical thermodynamics of a gas of charged particles in magnetic field
We will demonstrate that the paradox of classical statistical thermodynamics for a gas of charged particles in a magnetic field (GMF) has not yet been explained. The paradox lies in the statement that the average magnetic moment of a gas is zero, whereas the time-average magnetic moment of each pa...
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| Veröffentlicht in: | Condensed Matter Physics |
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| Datum: | 2006 |
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| Sprache: | English |
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Інститут фізики конденсованих систем НАН України
2006
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| Zitieren: | Classical statistical thermodynamics of a gas of charged particles in magnetic field / I.M. Dubrovskii // Condensed Matter Physics. — 2006. — Т. 9, № 1(45). — С. 23-36. — Бібліогр.: 19 назв. — англ. |
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Dubrovskii, I.M. 2017-06-13T20:22:28Z 2017-06-13T20:22:28Z 2006 Classical statistical thermodynamics of a gas of charged particles in magnetic field / I.M. Dubrovskii // Condensed Matter Physics. — 2006. — Т. 9, № 1(45). — С. 23-36. — Бібліогр.: 19 назв. — англ. 1607-324X PACS: 05.20.Gg, 75.20.-g DOI:10.5488/CMP.9.1.23 https://nasplib.isofts.kiev.ua/handle/123456789/121280 We will demonstrate that the paradox of classical statistical thermodynamics for a gas of charged particles in a magnetic field (GMF) has not yet been explained. The paradox lies in the statement that the average magnetic moment of a gas is zero, whereas the time-average magnetic moment of each particle is always negative. We consider a gas of charged particles moving in a plane perpendicular to a uniform magnetic field. The density of distribution of the ensemble describing statistical properties of the GMF is derived starting from the basics, with due regard for the specific character of dynamics of the charged particles in the magnetic field. It is emphasized that neither the imposition of a potential barrier restricting the existence region of the GMF, nor the introduction of a background neutralizing charge occupying a finite area, is a necessary condition for the stationary equilibrium state of the GMF to exist. We show that the reason for this fact is that the density of distribution of the ensemble is dependent, besides the Hamiltonian, on another positive definite integral of motion that is a linear combination of the Hamiltonian and the angular momentum of the GMF. Basic thermodynamic relations are deduced in terms of the new density of distribution, and it is demonstrated that the GMF has a magnetic moment whose magnitude and sign are determined by the external potential field. Particularly, the GMF is diamagnetic in the absence of the neutralizing background charge. Thus, the statement of the Bohr-van Leeuwen theorem, deduced using the ordinary Gibbs density of distribution depending on the Hamiltonian only, is wrong. It is noted that a great deal of works on the theory of electronic phenomena in magnetic field are based either on the same wrong density of distribution or on the formula for average occupation numbers depending on the energy of states, which follows from this density of distribution within quantum theory. These theories should be revised in view of the new form of the density of distribution en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Classical statistical thermodynamics of a gas of charged particles in magnetic field Класична статистична термодинаміка газу заряджених частинок у магнітному полі Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Classical statistical thermodynamics of a gas of charged particles in magnetic field |
| spellingShingle |
Classical statistical thermodynamics of a gas of charged particles in magnetic field Dubrovskii, I.M. |
| title_short |
Classical statistical thermodynamics of a gas of charged particles in magnetic field |
| title_full |
Classical statistical thermodynamics of a gas of charged particles in magnetic field |
| title_fullStr |
Classical statistical thermodynamics of a gas of charged particles in magnetic field |
| title_full_unstemmed |
Classical statistical thermodynamics of a gas of charged particles in magnetic field |
| title_sort |
classical statistical thermodynamics of a gas of charged particles in magnetic field |
| author |
Dubrovskii, I.M. |
| author_facet |
Dubrovskii, I.M. |
| publishDate |
2006 |
| language |
English |
| container_title |
Condensed Matter Physics |
| publisher |
Інститут фізики конденсованих систем НАН України |
| format |
Article |
| title_alt |
Класична статистична термодинаміка газу заряджених частинок у магнітному полі |
| description |
We will demonstrate that the paradox of classical statistical thermodynamics for a gas of charged particles
in a magnetic field (GMF) has not yet been explained. The paradox lies in the statement that the average
magnetic moment of a gas is zero, whereas the time-average magnetic moment of each particle is always
negative. We consider a gas of charged particles moving in a plane perpendicular to a uniform magnetic field.
The density of distribution of the ensemble describing statistical properties of the GMF is derived starting from
the basics, with due regard for the specific character of dynamics of the charged particles in the magnetic field.
It is emphasized that neither the imposition of a potential barrier restricting the existence region of the GMF,
nor the introduction of a background neutralizing charge occupying a finite area, is a necessary condition for
the stationary equilibrium state of the GMF to exist. We show that the reason for this fact is that the density
of distribution of the ensemble is dependent, besides the Hamiltonian, on another positive definite integral of
motion that is a linear combination of the Hamiltonian and the angular momentum of the GMF. Basic thermodynamic
relations are deduced in terms of the new density of distribution, and it is demonstrated that the
GMF has a magnetic moment whose magnitude and sign are determined by the external potential field. Particularly,
the GMF is diamagnetic in the absence of the neutralizing background charge. Thus, the statement
of the Bohr-van Leeuwen theorem, deduced using the ordinary Gibbs density of distribution depending on
the Hamiltonian only, is wrong. It is noted that a great deal of works on the theory of electronic phenomena
in magnetic field are based either on the same wrong density of distribution or on the formula for average
occupation numbers depending on the energy of states, which follows from this density of distribution within
quantum theory. These theories should be revised in view of the new form of the density of distribution
|
| issn |
1607-324X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/121280 |
| citation_txt |
Classical statistical thermodynamics of a gas of charged particles in magnetic field / I.M. Dubrovskii // Condensed Matter Physics. — 2006. — Т. 9, № 1(45). — С. 23-36. — Бібліогр.: 19 назв. — англ. |
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| first_indexed |
2025-12-07T21:15:23Z |
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2025-12-07T21:15:23Z |
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1850885666924134400 |