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arXiv · 2510.06795

Similarities and differences of typicality in quantum and classical systems

Peter Reimann·Nicolas Nessi
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Abstract

Typicality is a well-established and very general property of quantum many-body systems, referring to the phenomenon that the expectation values of any given observable are practically indistinguishable for the overwhelming majority of all pure states (normalized vectors) in a sufficiently high-dimensional Hilbert (sub-)space. Here, we provide very simple and general arguments that analogous typicality properties of pure states (phase space points) in classical many-body systems are still expected to hold true for macroscopic observables, but not any more for microscopic (few-body) observables.

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Peter Reimann, Nicolas Nessi. 2025-10-08. Similarities and differences of typicality in quantum and classical systems. https://doi.org/10.1515/zna-2025-0391

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