.. _sphx_glr_api_gallery_statphys_ehrenfest_urn:

Ehrenfest urn
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Reversible microscopic dynamics and the emergence of an arrow of time.


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    <div class="sphx-glr-thumbcontainer" tooltip="Two objections were raised against Boltzmann&#x27;s H-theorem soon after he proposed it: Loschmidt argued that time-reversible microscopic dynamics cannot produce genuinely irreversible macroscopic behavior, and Zermelo noted that any bounded mechanical system must (by Poincare recurrence) eventually return arbitrarily close to its initial state. The Ehrenfests&#x27; 1907 urn model resolves both at once, in the simplest possible setting.">

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  :doc:`/api/gallery/statphys/ehrenfest_urn/plot_ehrenfest_irreversibility`

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      <div class="sphx-glr-thumbnail-title">The Ehrenfest urn: reversibility, recurrence, and the arrow of time</div>
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   /api/gallery/statphys/ehrenfest_urn/plot_ehrenfest_irreversibility