Undecidability in Physics: a Review
Mathematical Physics
2025-07-17 v2 Strongly Correlated Electrons
math.MP
Quantum Physics
Abstract
The study of undecidability in problems arising from physics has experienced a renewed interest, mainly in connection with quantum information problems. The goal of this review is to survey this recent development. After a historical introduction, we first explain the necessary results about undecidability in mathematics and computer science. Then we briefly review the first results about undecidability in physics which emerged mostly in the 80s and early 90s. Finally we focus on the most recent contributions, which we divide in two main categories: many body systems and quantum information problems.
Cite
@article{arxiv.2410.16532,
title = {Undecidability in Physics: a Review},
author = {Álvaro Perales-Eceiza and Toby Cubitt and Mile Gu and David Pérez-García and Michael M. Wolf},
journal= {arXiv preprint arXiv:2410.16532},
year = {2025}
}
Comments
72 pages, v2