DOI: 10.1063/1.1666370. On the relationship between bifurcation points of the Kirkwood-Salsburg equation and phase transitions

On the relationship between bifurcation points of the Kirkwood-Salsburg equation and phase transitions

10.1063/1.1666370

Crossref journal-article

AIP Publishing

Journal of Mathematical Physics (317)

Abstract

In this paper we explore the Vlasov conjecture on the relationship between bifurcation points and phase transitions. Because of the availability of the exact results of Ruelle, we focus our attention on the Kirkwood-Salsburg hierarchy, and recognizing that the first equation in this hierarchy is of the form of a Lichtenstein-Lyapunov nonlinear operator equation, we use a fundamental theorem of Krasnosel'skii to determine, under a suitable closure, bifurcation points for the same system considered by Ruelle. A special example is treated—that of a one-dimensional system of hard rods— and our main conclusion follows from the results of this study: namely, that ``in this one-dimensional system'' the bifurcation point does not seem to be related to the onset of a phase transition.

Bibliography

Cheng, I.-Y. S., & Kozak, J. J. (1973). On the relationship between bifurcation points of the Kirkwood-Salsburg equation and phase transitions. Journal of Mathematical Physics, 14(5), 632â637.

Authors 2

Ing-Yih S. Cheng (first)
John J. Kozak (additional)

References 21 Referenced 9

10.1063/1.1750949 / J. Chem. Phys. (1941)
{'key': '2024020602511447900_r2'}
10.1063/1.1673324 / J. Chem. Phys. (1970)
{'key': '2024020602511447900_r4'}
{'key': '2024020602511447900_r4a'}
{'key': '2024020602511447900_r5', 'first-page': '26', 'volume': '5', 'year': '1963', 'journal-title': 'Fiz. Tverd. Tela'} / Fiz. Tverd. Tela (1963)
{'key': '2024020602511447900_r5a', 'first-page': '16', 'volume': '5', 'year': '1963', 'journal-title': 'Sov. Phys.-Solid State'} / Sov. Phys.-Solid State (1963)
10.1103/PhysRev.138.A1346 / Phys. Rev. A (1965)
10.1016/0031-8914(65)90142-4 / Physica (Utr.) (1965)
10.1016/0031-8914(66)90080-2 / Physica (Utr.) (1966)
10.1016/0031-8914(71)90091-7 / Physica (Utr.) (1971)
10.1016/0031-9163(62)90198-1 / Phys. Lett. (1962)
10.1063/1.1703906 / J. Math. Phys. (1963)
10.1063/1.1704186 / J. Math. Phys. (1964)
{'key': '2024020602511447900_r8'}
{'key': '2024020602511447900_r9'}
{'key': '2024020602511447900_r10', 'first-page': '345', 'volume': '10', 'year': '1958', 'journal-title': 'Am. Math. Soc. Transl.'} / Am. Math. Soc. Transl. (1958)
{'key': '2024020602511447900_r11'}
10.1016/0003-4916(63)90336-1 / Ann. Phys. (N.Y.) (1963)
10.1103/PhysRev.87.404 / Phys. Rev. (1952)
10.1103/PhysRev.50.955 / Phys. Rev. (1936)

Dates

Type	When
Created	21 years, 6 months ago (Feb. 10, 2004, 12:31 p.m.)
Deposited	1 year, 6 months ago (Feb. 5, 2024, 9:51 p.m.)
Indexed	1 year, 6 months ago (Feb. 9, 2024, 11:29 a.m.)
Issued	52 years, 4 months ago (May 1, 1973)
Published	52 years, 4 months ago (May 1, 1973)
Published Print	52 years, 4 months ago (May 1, 1973)

Funders 0

None

BibTeX

@article{Cheng_1973, title={On the relationship between bifurcation points of the Kirkwood-Salsburg equation and phase transitions}, volume={14}, ISSN={1089-7658}, url={http://dx.doi.org/10.1063/1.1666370}, DOI={10.1063/1.1666370}, number={5}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Cheng, Ing-Yih S. and Kozak, John J.}, year={1973}, month=may, pages={632–637} }

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