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Symmetry-Driven Thermalization via Finite de Finetti Theorems

Uttam Singh ^1,2,* and Nicolas J. Cerf^3,†

¹Centre for Quantum Science and Technology (CQST), International Institute of Information Technology Hyderabad, Gachibowli 500032, Telangana, India
²Center for Security, Theory and Algorithmic Research (CSTAR), International Institute of Information Technology Hyderabad, Gachibowli 500032, Telangana, India
³Centre for Quantum Information and Communication, École polytechnique de Bruxelles, CP 165, Université libre de Bruxelles, 1050 Brussels, Belgium

^*Contact author: uttam@iiit.ac.in
^†Contact author: nicolas.cerf@ulb.be

Phys. Rev. Lett. 137, 100402 – Published 2 September, 2026

DOI: https://doi.org/10.1103/df89-tdks

Abstract

Thermal behavior in subsystems of closed quantum systems is commonly attributed to dynamical chaos, quantum ergodicity, canonical typicality, or the eigenstate thermalization hypothesis, suggesting a fundamentally statistical origin of thermalization. Here, we propose a potential alternative mechanism in which thermal structures emerge deterministically from symmetry considerations alone, without recourse to statistical arguments. We prove a finite de Finetti–type theorem for quantum states invariant under energy-preserving unitaries, establishing that the reduced marginals of any such invariant $N$ -qudit state are close (both in trace distance and relative entropy) to convex mixtures of thermal product states, with explicit error bounds vanishing as $N \to \infty$ . We further present an example of Lindblad dynamics whose longtime limit is invariant under energy-preserving unitaries, providing a dynamical realization of the desired symmetry class. These results imply that invariance under energy-preserving unitaries suffices as a sole fundamental, deterministic principle to enforce thermal structures.

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Symmetry-Driven Thermalization via Finite de Finetti Theorems

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