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Irreversibility from staircases in symplectic embeddings

Author

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  • Creaco, Anthony J.
  • Kalogeropoulos, Nikolaos

Abstract

We present an argument whose goal is to trace the origin of the macroscopically irreversible behavior of Hamiltonian systems of many degrees of freedom. We use recent flexibility and rigidity results of symplectic embeddings, quantified via the (stabilized) Fibonacci and Pell staircases, to encode the underlying breadth of the possible initial conditions, which alongside the multitude of degrees of freedom of the underlying system give rise to time-irreversibility.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:513:y:2019:i:c:p:497-509
    DOI: 10.1016/j.physa.2018.09.047
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    References listed on IDEAS

    as
    1. Kalogeropoulos, Nikolaos, 2018. "Time irreversibility from symplectic non-squeezing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 202-210.
    2. Kalogeropoulos, Nikos, 2012. "Tsallis entropy induced metrics and CAT(k) spaces," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3435-3445.
    3. Cerino, L. & Cecconi, F. & Cencini, M. & Vulpiani, A., 2016. "The role of the number of degrees of freedom and chaos in macroscopic irreversibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 486-497.
    4. Lebowitz, Joel L., 1999. "Microscopic origins of irreversible macroscopic behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 516-527.
    5. Zakharov, A.Yu., 2017. "Determinism vs. statistics in classical many-body theory: Dynamical origin of irreversibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 72-76.
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    Cited by:

    1. Kalogeropoulos, Nikolaos, 2020. "Toward a relative q-entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    2. Kalogeropoulos, Nikolaos, 2022. "Coarse-graining and symplectic non-squeezing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 589(C).

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