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Ergodicity and hydrodynamics: From quantum to classical spin systems

Jiaozi Wang1,*, Luca Capizzi2,*, Dario Poletti3,4,5,6,†, and Leonardo Mazza2,7,‡

  • *These authors contributed equally to this work.
  • †Contact author: dario_poletti@sutd.edu.sg
  • ‡Contact author: leonardo.mazza@universite-paris-saclay.fr
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Phys. Rev. E 113, 064102 – Published 1 June, 2026

DOI: https://doi.org/10.1103/mm75-dmt4

Abstract

We show that in classical spin systems, the precise nature of the late-time hydrodynamic tails of the autocorrelation functions of a generic observable is determined by (i) the dynamical critical exponent and (ii) the equilibrium thermodynamic properties of the corresponding observable. We provide numerical results for one- and two-dimensional systems and present theoretical considerations that only rely on the notion of ergodicity. Our result extends to the classical framework the relaxation-overlap inequality, first introduced in [Phys. Rev. X 15, 011059 (2025)] for quantum many-body systems satisfying the eigenstate thermalization hypothesis.

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Phys. Rev. E 113, 064102– Published 1 June, 2026
  • Received 3 October 2025
  • Accepted 15 May 2026
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