Necessity of entanglement for the typicality argument in statistical mechanics

Abstract:Typicality arguments replace the postulated mixed state ensembles of statistical mechanics with pure states sampled uniformly at random, explaining why most microstates of large systems exhibit thermal behavior. This paradigm has been revived in quantum contexts, where entanglement is deemed essential, but no clear quantitative link between entanglement structure and typicality has been established. Here, we study pure quantum states with controlled multipartite entanglement and show that when entanglement grows with system size $N$, fluctuations in macroscopic observables decay exponentially with $N$, whereas if entanglement remains finite, one recovers only the classical $1/\sqrt{N}$ suppression. Our work thus provides a quantitative connection between entanglement structure and the emergence of typicality, demonstrating that entanglement is crucial for thermalization in small quantum systems but unnecessary to justify equilibrium in macroscopic ensembles. This unifies classical and quantum foundations of statistical mechanics by pinpointing exactly when and why entanglement matters.

5 pages, 1 figure. Published as a Letter in Phys. Rev. A. Comments are welcome

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2504.21090 [quant-ph]

(or arXiv:2504.21090v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2504.21090 Focus to learn more arXiv-issued DOI via DataCite

Phys. Rev. A 113, L060202 (2026)

https://doi.org/10.1103/nhvg-ckc6 Focus to learn more DOI(s) linking to related resources

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.