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Ergodic observables in non-ergodic systems: The example of the harmonic chain

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  • Baldovin, Marco
  • Marino, Raffaele
  • Vulpiani, Angelo

Abstract

In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence between time averages and ensemble averages. This property can be proved only for a limited number of systems; however, as proved by Khinchin (1949), weak forms of it hold even in systems that are not ergodic at the microscopic scale, provided that extensive observables are considered.

Suggested Citation

  • Baldovin, Marco & Marino, Raffaele & Vulpiani, Angelo, 2023. "Ergodic observables in non-ergodic systems: The example of the harmonic chain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    • Handle: RePEc:eee:phsmap:v:630:y:2023:i:c:s0378437123008282
    DOI: 10.1016/j.physa.2023.129273
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    References listed on IDEAS

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    1. Cocciaglia, Niccolò & Vulpiani, Angelo & Gradenigo, Giacomo, 2022. "Thermalization without chaos in harmonic systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 601(C).
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