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Coarse-graining and symplectic non-squeezing

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  • Kalogeropoulos, Nikolaos

Abstract

We address aspects of coarse-graining in classical Statistical Physics from the viewpoint of the symplectic non-squeezing theorem. We make some comments regarding the implications of the symplectic non-squeezing theorem for the BBGKY hierarchy. We also see the cubic cells appearing in coarse-graining as a direct consequence of the uniqueness of Hofer’s metric on the group of Hamiltonian diffeomorphisms of the phase space.

Suggested Citation

  • Kalogeropoulos, Nikolaos, 2022. "Coarse-graining and symplectic non-squeezing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).
    • Handle: RePEc:eee:phsmap:v:589:y:2022:i:c:s0378437121009328
    DOI: 10.1016/j.physa.2021.126720
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    References listed on IDEAS

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    1. Swendsen, Robert H., 2017. "The definition of the thermodynamic entropy in statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 67-73.
    2. Creaco, Anthony J. & Kalogeropoulos, Nikolaos, 2019. "Irreversibility from staircases in symplectic embeddings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 497-509.
    3. Lebowitz, Joel L., 1993. "Macroscopic laws, microscopic dynamics, time's arrow and Boltzmann's entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 194(1), pages 1-27.
    4. Kalogeropoulos, Nikolaos, 2018. "Time irreversibility from symplectic non-squeezing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 202-210.
    5. Matty, Michael & Lancaster, Lachlan & Griffin, William & Swendsen, Robert H., 2017. "Comparison of canonical and microcanonical definitions of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 474-489.
    6. Swendsen, Robert H. & Wang, Jian-Sheng, 2016. "Negative temperatures and the definition of entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 24-34.
    Full references (including those not matched with items on IDEAS)

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