Das (2602.21149) shows that classical many-body systems with local interactions have upper bounds on how chaotic they can be — and the tightest bound becomes independent of temperature in the thermodynamic limit.
Chaotic instability is quantified by the largest Lyapunov exponent: the rate at which nearby trajectories diverge. In quantum systems, the Maldacena-Shenker-Stanford bound provides a universal ceiling on chaos growth tied to temperature. No such universal bound exists for classical systems. Das provides the next best thing: explicit, Hamiltonian-specific bounds that depend on inertia and interaction geometry.
The bounds separate into two classes. Non-violable bounds are set by worst-case local curvature of the interaction potential and are insensitive to spatial structure — they hold instantaneously regardless of the system's state. Ergodic ceilings are tighter: they retain spectral information about collective modes and finite-size effects and hold under generic dynamical evolution. The ergodic ceiling captures collective suppression mechanisms that the non-violable bound misses.
For a one-dimensional coupled-rotor chain (a Josephson junction array), the ergodic ceiling has a closed analytic form. It creates a dynamically inaccessible region in the Lyapunov exponent-energy plane — a forbidden zone that the system cannot sustain chaotic growth into. Numerics confirm the prediction.
The striking result: in the thermodynamic limit, the ergodic ceiling approaches an inertial ceiling that depends only on the particle mass and interaction range, independent of temperature and coupling strength. The system's maximum chaos rate is set by its inertia — how quickly particles can respond to forces — and the geometry of their interactions. Heat the system arbitrarily and the chaos ceiling stays fixed. The memory of initial conditions has a minimum lifetime determined by mass and geometry alone.