Classical billiards can compute

• Published in 2025
• Added on 2026-01-12

We show that two-dimensional billiard systems are Turing complete by encoding their dynamics within the framework of Topological Kleene Field Theory. Billiards serve as idealized models of particle motion with elastic reflections and arise naturally as limits of smooth Hamiltonian systems under steep confining potentials. Our results establish the existence of undecidable trajectories in physically natural billiard-type models, including billiard-type models arising in hard-sphere gases and in collision-chain limits of celestial mechanics.

Links

• https://arxiv.org/abs/2512.19156v2
• https://arxiv.org/pdf/2512.19156v2

Other information

BibTeX entry

@article{Classicalbilliardscancompute,
	key = {Classicalbilliardscancompute},
	type = {article},
	title = {Classical billiards can compute},
	author = {Eva Miranda and Isaac Ramos},
	abstract = {We show that two-dimensional billiard systems are Turing complete by encoding their dynamics within the framework of Topological Kleene Field Theory. Billiards serve as idealized models of particle motion with elastic reflections and arise naturally as limits of smooth Hamiltonian systems under steep confining potentials. Our results establish the existence of undecidable trajectories in physically natural billiard-type models, including billiard-type models arising in hard-sphere gases and in collision-chain limits of celestial mechanics.},
	comment = {},
	date_added = {2026-01-12},
	date_published = {2025-01-12},
	urls = {https://arxiv.org/abs/2512.19156v2,https://arxiv.org/pdf/2512.19156v2},
	collections = {unusual-computers},
	url = {https://arxiv.org/abs/2512.19156v2 https://arxiv.org/pdf/2512.19156v2},
	year = 2025,
	urldate = {2026-01-12},
	archivePrefix = {arXiv},
	eprint = {2512.19156},
	primaryClass = {math.DS}
}