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Archimedes’ Principle for Ideal Gas

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Abstract

We prove Archimedes’ principle for a macroscopic ball in ideal gas consisting of point particles with non-zero mass. The main result is an asymptotic theorem, as the number of point particles goes to infinity and their total mass remains constant. We also show that, asymptotically, the gas has an exponential density as a function of height. We find the asymptotic inverse temperature of the gas. We derive an accurate estimate of the volume of the phase space using the local central limit theorem.

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Acknowledgements

We are grateful to Shuntao Chen, Persi Diaconis, Martin Hairer, Robert Hołyst, Werner Krauth, Mathew Penrose and David Ruelle for the most useful advice. We thank the anonymous referees for suggestions for improvement.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195, USA

    Krzysztof Burdzy

  2. Department of Mathematics, Wrocław University of Science and Technology, ul. Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Jacek Małecki

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  1. Krzysztof Burdzy
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  2. Jacek Małecki
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Correspondence to Krzysztof Burdzy.

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Communicated by M. Hairer.

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KB’s research was supported in part by Simons Foundation Grant 506732. J. Małecki was supported by the Polish National Science Centre (NCN) grant no. 2018/29/B/ST1/02030.

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Burdzy, K., Małecki, J. Archimedes’ Principle for Ideal Gas. Commun. Math. Phys. 392, 185–217 (2022). https://doi.org/10.1007/s00220-022-04347-4

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