Chemical reactions can be blocked not by a lack of energy, but by a 'geometric ghost' that prevents molecules from squeezing through certain shapes.
April 14, 2026
Original Paper
Symplectic Constraints in Classical Reaction Dynamics: From Gromov's Camel to Reaction Rates
arXiv · 2604.10408
The Takeaway
It applies a deep math theorem called 'Gromov's Camel' to show that the shape of a molecule’s state space is just as important as how much heat you apply. Even with enough energy, a reaction can be delayed indefinitely simply because the particles can't 'fit' through the required phase-space trajectory.
From the abstract
We investigate whether ideas from symplectic topology, in particular Gromov's non-squeezing theorem and symplectic capacity, can provide useful geometric insight into classical reaction dynamics near an index-1 saddle. Using Poincaré-Birkhoff normal form theory, we describe the phase-space structures that organize transport through the transition-state region, including dividing surfaces, normally hyperbolic invariant manifolds (NHIMs), and the associated bath-action geometry. For quadratic sadd