Deriving the Eigenstate Thermalization Hypothesis from Eigenstate Typicality and Kinematic Principles

• URL: http://arxiv.org/abs/2512.13348v2
• Date: Sun, 21 Dec 2025 03:30:13 GMT
• Title: Deriving the Eigenstate Thermalization Hypothesis from Eigenstate Typicality and Kinematic Principles
• Authors: Yucheng Wang,
• Abstract summary: The eigenstate thermalization hypothesis (ETH) provides a powerful framework for understanding thermalization in isolated quantum many-body systems.<n>We derive the structure of ETH from a minimal dynamical principle, which we term the eigenstate typicality principle (ETP)<n>Our results establish ETH as a consequence of entropy, Hilbert-space geometry, and chaos-induced eigenstate typicality.
• Score: 5.749848575482736
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The eigenstate thermalization hypothesis (ETH) provides a powerful framework for understanding thermalization in isolated quantum many-body systems, yet a complete and conceptually transparent derivation has remained elusive. In this work, we derive the structure of ETH from a minimal dynamical principle, which we term the eigenstate typicality principle (ETP), together with general kinematic ingredients arising from entropy maximization, Hilbert-space geometry, and locality. ETP asserts that in quantum-chaotic systems, energy eigenstates are statistically indistinguishable, with respect to local measurements, from states drawn from the Haar measure on a narrow microcanonical shell. Within this framework, diagonal ETH arises from concentration of measure, provided that eigenstate typicality holds. The structure of off-diagonal matrix elements is then fixed by entropic scaling and the finite-time dynamical correlations of local observables, with ETP serving as the dynamical bridge to energy eigenstates, without invoking random-matrix assumptions. Our results establish ETH as a consequence of entropy, Hilbert-space geometry, and chaos-induced eigenstate typicality, and clarify its regime of validity across generic quantum-chaotic many-body systems, thereby deepening our understanding of quantum thermalization and the emergence of statistical mechanics from unitary many-body dynamics.

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