Computable Ergodic Optimisation
Abstract
Links between physicals systems and computability properties have been an active field of investigation in recent years. Inspired by a previous work in the context of positive temperature Gibbs measures, we prove here that in the context of zero-temperature ergodic optimisation, for a computable potential and provided with several reasonable assumptions, the maximum ergodic average is a computable real number, and the set of maximising measures is a Π1-computable compact set. Then, in the more specific context of symbolic dynamics, with finite-range interactions on subshifts of finite type, we provide an explicit algorithm to compute both the maximum ergodic average and the set of maximising measures in finite time, with a matching code repository.
Related
- The computable functional calculus
- Computable presentations of reduced group C*-algebras of hyperbolic groups
- Computable presentations of reduced group C*-algebras of groups with the rapid decay property
- Non-aware computable presentations of randomizations
- Computable presentations of separable Lebesgue spaces
BibTeX
@misc{gayral2026computable,
title = {{Computable Ergodic Optimisation}},
author = {Léopoldine Gayral and Mathieu Hoyrup},
howpublished = {arXiv},
year = {2026},
month = jul,
doi = {10.48550/arxiv.2607.11404},
eprint = {2607.11404},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.11404},
}
RIS
TY - UNPB
TI - Computable Ergodic Optimisation
AU - Léopoldine Gayral
AU - Mathieu Hoyrup
PY - 2026
DA - 2026/07/13
PB - arXiv
DO - 10.48550/arxiv.2607.11404
UR - https://arxiv.org/abs/2607.11404
AB - Links between physicals systems and computability properties have been an active field of investigation in recent years. Inspired by a previous work in the context of positive temperature Gibbs measures, we prove here that in the context of zero-temperature ergodic optimisation, for a computable potential and provided with several reasonable assumptions, the maximum ergodic average is a computable real number, and the set of maximising measures is a Π_1-computable compact set. Then, in the more specific context of symbolic dynamics, with finite-range interactions on subshifts of finite type, we provide an explicit algorithm to compute both the maximum ergodic average and the set of maximising measures in finite time, with a matching code repository.
ER -