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A topological fluctuation theorem

Author

Listed:
  • Benoît Mahault

    (Max Planck Institute for Dynamics and Self-Organization)

  • Evelyn Tang

    (Max Planck Institute for Dynamics and Self-Organization)

  • Ramin Golestanian

    (Max Planck Institute for Dynamics and Self-Organization
    University of Oxford)

Abstract

Fluctuation theorems specify the non-zero probability to observe negative entropy production, contrary to a naive expectation from the second law of thermodynamics. For closed particle trajectories in a fluid, Stokes theorem can be used to give a geometric characterization of the entropy production. Building on this picture, we formulate a topological fluctuation theorem that depends only by the winding number around each vortex core and is insensitive to other aspects of the force. The probability is robust to local deformations of the particle trajectory, reminiscent of topologically protected modes in various classical and quantum systems. We demonstrate that entropy production is quantized in these strongly fluctuating systems, and it is controlled by a topological invariant. We demonstrate that the theorem holds even when the probability distributions are non-Gaussian functions of the generated heat.

Suggested Citation

  • Benoît Mahault & Evelyn Tang & Ramin Golestanian, 2022. "A topological fluctuation theorem," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-30644-6
    DOI: 10.1038/s41467-022-30644-6
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    References listed on IDEAS

    as
    1. Kazuki Sone & Yuto Ashida & Takahiro Sagawa, 2020. "Exceptional non-Hermitian topological edge mode and its application to active matter," Nature Communications, Nature, vol. 11(1), pages 1-11, December.
    2. Arvind Murugan & Suriyanarayanan Vaikuntanathan, 2017. "Topologically protected modes in non-equilibrium stochastic systems," Nature Communications, Nature, vol. 8(1), pages 1-6, April.
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