Ergodicity and hydrodynamics: from quantum to classical spin systems

• URL: http://arxiv.org/abs/2509.04098v1
• Date: Thu, 04 Sep 2025 10:59:57 GMT
• Title: Ergodicity and hydrodynamics: from quantum to classical spin systems
• Authors: Jiaozi Wang, Luca Capizzi, Dario Poletti, Leonardo Mazza,
• Abstract summary: We show that 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.<n>We provide numerical results for one- and two-dimensional systems and present theoretical considerations that only rely on the notion of ergodicity.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 Capizzi et al. Phys. Rev. X 15, 011059 (2025)] for quantum many-body systems satisfying the eigenstate thermalization hypothesis.

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