Symmetry-driven thermalization via finite de Finetti theorems

TL;DR

This paper demonstrates that thermalization in quantum systems can emerge deterministically from symmetry considerations alone, without relying on statistical or chaotic assumptions.

Contribution

It proves a finite de Finetti theorem for energy-preserving invariant quantum states, linking symmetry to thermal structure without statistical arguments.

Findings

Reduced marginals approximate convex mixtures of thermal states

Explicit error bounds vanish as system size increases

Long-time limit of certain dynamics is invariant under energy-preserving unitaries

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.