Chaos Without Disorder: Why Entropy Doesn't Grow express
Hundreds of cooks in a kitchen — total chaos. Usually disorder grows. In quantum physics, the measure of such disorder is called entropy John von Neumann. For a many-particle system, entropy typically increases with their number. But scientists have found an exception.
The secret lies in a strict rule: two cooks cannot enter the same aisle at the same time. This blockade is familiar from Rydberg atoms: neighboring particles cannot occupy the same state. Because of this, the entropy does not exceed ln 2 (about 0.7), as if a huge kitchen behaves like a tiny nook.
The result changes the view on quantum chaos. Not only energy is important, but also the geometry of the space where particles live. The authors propose building systems with a given limit of entropy, which opens the way to new quantum devices.
Original abstract
as written by the authors arXiv:2510.27511
Entanglement entropy is a fundamental diagnostic for quantum chaos, typically exhibiting volume-law scaling in highly excited eigenstates of chaotic many-body systems. In this work, we present a striking counterexample: a Floquet-driven quantum many-body system with Rydberg-like blockade that, despite being fully chaotic as indicated by its Wigner-Dyson level statistics and local thermalization, exhibits a strict area-law entanglement entropy. Specifically, the entanglement entropy of every Floquet eigenstate is bounded by $$\ln2$$, independent of system size. We trace this anomaly to the specific Hilbert space structure imposed by the blockades, which restricts the Schmidt rank across a bipartition. Furthermore, we generalize this discovery by establishing a duality between constrained many-body Hamiltonians and single-particle quantum walks on median graphs, and we outline a general procedure for constructing systems with an entanglement entropy bounded by a predetermined constant. Our results demonstrate that entanglement entropy alone is an insufficient diagnostic of many-body quantum chaos and highlight the profound impact of Hilbert space geometry on quantum dynamics and thermalization.
Rydberg atoms, which inspired this work, are giant atoms swollen to the size of bacteria. Their electrons are so far from the nucleus that the atoms can 'feel' each other at huge distances.
The idea that complex systems can hide rigid constraints is reminiscent of Liu Cixin's novel 'The Three-Body Problem,' where outwardly unpredictable chaos obeys hidden laws.