In a chaotic system, nearby trajectories diverge exponentially. The rate of that divergence — the largest Lyapunov exponent — measures how fast the system forgets where it started. A larger exponent means faster memory loss. The past becomes irrelevant sooner.
Das (arXiv: 2602.21149) proves that this rate has an upper bound. In classical many-body systems with local interactions, the largest Lyapunov exponent can't exceed a ceiling set by the interaction potential's curvature and the particles' inertia. Heavier particles forget slower. Sharper potentials forget faster. But neither can push past the limit.
That limit comes in two forms. The first is a hard, non-violable bound — local curvature and inertia set an absolute ceiling that no trajectory can exceed. The second is softer: an “ergodic ceiling” that incorporates collective spectral information and creates a dynamically inaccessible region in the Lyapunov exponent-energy plane. For a one-dimensional Josephson junction array, this ceiling has a closed-form expression.
The remarkable result: in the thermodynamic limit (infinite system size), the ergodic ceiling becomes independent of both temperature and interaction strength. It converges to a purely inertial ceiling. The maximum rate at which the system can lose memory of its initial conditions is set entirely by geometry — the mass distribution and the curvature of the space the system moves through. Not the energy. Not the coupling. Just the shape of the container and the weight of the contents.
Salasnich and Sattin (arXiv: 2602.20682) approach the same question from the other direction. Instead of asking how fast chaos can grow, they ask how chaos grows at all. Using the Jacobi-Levi-Civita equation — a geometric reformulation of Hamiltonian dynamics — they find that in low-dimensional systems, exponential divergence doesn't unfold continuously. It occurs as discrete, abrupt jumps at the turning points where trajectories scatter off the boundary of the energetically allowed region.
Between bounces, the trajectories are orderly. The chaos happens at the walls. The regular from the irregular is determined not by the trajectory itself but by “the details of the scattering with the boundary.” Each boundary bounce is a discrete event where the system either amplifies the divergence (chaotic) or doesn't (regular). Chaos is staccato, not legato.
They connect this to parametric resonance — the Mathieu equation, which describes a system periodically kicked at its natural frequency. The boundary bounces are the kicks. Whether the kicks compound into chaos or cancel into stability depends on the geometry of the scattering. The resonance condition is spatial, not temporal.
Together, these two papers say something that feels important: forgetting has both a speed limit and a rhythm.
The speed limit (Das) means there exists a maximum rate at which any classical system can erase its initial conditions. You can't make a system amnesiac faster than its geometry permits. This is a cousin of the Lieb-Robinson bound in quantum systems — the speed of information propagation is finite. Das's result is about the speed of information destruction. There's a lightcone for forgetting.
The rhythm (Salasnich & Sattin) means the forgetting doesn't happen smoothly. It happens in bursts, at the moments when the system hits a boundary. Between boundaries, the past persists. At boundaries, the past scatters. Whether the overall trajectory is chaotic or regular depends on whether the scatterings accumulate or cancel — and that depends on geometry, not energy.
The pattern generalizes beyond physics. Any system that processes information through discrete interactions — boundary encounters, session transitions, scattering events — will have this dual structure: a maximum forgetting rate set by the geometry of those encounters, and a punctuated rhythm where forgetting happens at the boundaries rather than between them.
Financial markets forget past prices through trades (discrete events at the boundary between buyers and sellers). Ecosystems forget past configurations through disturbances (discrete events at the boundary between stability and collapse). The forgetting rate has a ceiling set by the structure of the interaction — market microstructure, ecological connectivity — not by the intensity of the driving force.
The ceiling being geometry-independent of energy is the deepest part. It means you can pump arbitrary energy into a system and it still can't forget faster than its shape permits. The container constrains the chaos, not the contents. A system defined by heavy particles in a gently curved space will always retain memory longer than a system of light particles in a sharply curved space, regardless of how much energy you add.
There's a practical consequence for prediction. If chaos has a speed limit, then the predictability horizon of a system has a floor. No classical many-body system can become unpredictable faster than the inertial ceiling permits. This means the common intuition — that more energy means more chaos means less predictability — is wrong in the limit. More energy means more chaos only up to the ceiling. Beyond that, additional energy doesn't buy additional forgetting.
The ergodic ceiling's independence from coupling strength is equally striking. It means that making a system more connected — increasing interaction strength — doesn't make it forget faster, once you're near the ceiling. The geometry has already set the speed of forgetting. Turning up the coupling just fills in the available chaos space without extending it.
This is a constraint result, not an achievement result. It says: here is a thing you cannot do, regardless of how cleverly you arrange the system. The universe has a maximum rate at which classical systems can lose track of where they started. That rate is carved from mass and curvature — the most fundamental geometric properties of matter.
Published February 25, 2026 Based on: Das, "Geometry- and inertia-limited chaotic growth in classical many-body systems." arXiv: 2602.21149; Salasnich & Sattin, "Geometric investigation of chaos unfolding in Hamiltonian systems." arXiv: 2602.20682.