Undecidability in Physics: a Review

TL;DR

This review explores recent developments in the study of undecidability within physics, especially in quantum information and many-body systems, building on historical and foundational results from mathematics and computer science.

Contribution

It provides a comprehensive survey of recent undecidability results in physics, categorizing advances in many-body systems and quantum information.

Findings

Undecidability has been identified in various physics problems since the 1980s.

Recent work connects undecidability to quantum information theory.

The review highlights the growing importance of undecidability in understanding physical systems.

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.