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Einstein’s Approach to Statistical Mechanics: The 1902–04 Papers

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Abstract

We summarize the papers published by Einstein in the Annalen der Physik in the years 1902–1904 on the derivation of the properties of thermal equilibrium on the basis of the mechanical equations of motion and of the calculus of probabilities. We point out the line of thought that led Einstein to an especially economical foundation of the discipline, and to focus on fluctuations of the energy as a possible tool for establishing the validity of this foundation. We also sketch a comparison of Einstein’s approach with that of Gibbs, suggesting that although they obtained similar results, they had different motivations and interpreted them in very different ways.

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Notes

  1. This is the fundamental hypothesis linking the mechanical and the statistical aspects of the problem. It is probably inspired by the consideration of monocyclic systems, introduced by Helmholtz [17] and discussed by Boltzmann in [18–20]. Cf. [21] and [22].

  2. Einstein actually considers two systems with the same number of degrees of freedom, but where the energy contained in \(\varSigma \) is considerably larger. Apparently the equipartition theorem, which he derives in Sect. 6 of the paper, led him to realize the awkwardness of this restriction, and he drops it in the second paper.

  3. Einstein actually uses the notation 2h instead of \(\beta \), which is now the traditional choice.

  4. This will be the starting point of his 1903 paper.

  5. It is the relation now known as Jean’s radiation law.

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Acknowledgments

LP was introduced to critical phenomena by Leo’s lectures in the 1971 Varenna School, and RR fondly remembers Leo’s course in the Escuela Mexicana de Física Estadística, which had a great influence on the Statistical Physics group at UNAM. Both authors dedicate this work to Leo’s memory. LP is grateful to Jeferson Arenzon for encouraging him to present his ideas on Einstein’s 1902–1904 works.

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Authors and Affiliations

  1. Simons Center for Systems Biology, Institute for Advanced Study, Einstein Drive, Princeton, NJ, 08540, USA

    Luca Peliti

  2. Instituto de Energías Renovables, Universidad Nacional Autónoma de México, Priv. Xochicalco S/N, 62580, Temixco, Morelos, Mexico

    Raúl Rechtman

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  1. Luca Peliti
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Correspondence to Luca Peliti.

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Peliti, L., Rechtman, R. Einstein’s Approach to Statistical Mechanics: The 1902–04 Papers. J Stat Phys 167, 1020–1038 (2017). https://doi.org/10.1007/s10955-016-1615-8

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