Symmetry-driven thermalization via finite de Finetti theorems

• URL: http://arxiv.org/abs/2604.09410v1
• Date: Fri, 10 Apr 2026 15:24:21 GMT
• Title: Symmetry-driven thermalization via finite de Finetti theorems
• Abstract summary: We prove a finite de Finetti-type theorem for quantum states invariant under energy-preserving unitaries.<n>We present an example of energy-conserving Lindblad dynamics whose long-time limit is invariant under energy-preserving unitaries.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 energy-conserving Lindblad dynamics whose long-time 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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