Abstract
In this paper I combine techniques recently developed by Charles Fefferman with the well-known methods of Joel Lebowitz and Elliott Lieb to resolve some technical problems left unsettled by Lebowitz and Lieb's fundamental 1972 paper “The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei.”
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References
J. Lebowitz and E. Lieb, Existence of thermodynamics for real matter with Coulomb forces,Phys. Rev. Lett. 22(13):631 (1969); E. Lieb and J. Lebowitz, The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei.Adv. Math. 9:316 (1972).
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C. Fefferman, The thermodynamic limit for a crystal,Commun. Math. Phys. (to appear).
J. Lebowitz and R. Pena, Low density form of the free energy for real matter,J. Chem. Phys. 59(3):1362 (1973).
M. E. Fischer, The free energy of a macroscopic system,Arch. Rat. Mech. Anal. 17:377 (1964).
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Hughes, W. Thermodynamics for Coulomb systems: A problem at vanishing particle densities. J Stat Phys 41, 975–1013 (1985). https://doi.org/10.1007/BF01010012
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DOI: https://doi.org/10.1007/BF01010012