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 -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.
Cite
@article{arxiv.2607.11404,
title = {Computable Ergodic Optimisation},
author = {Léo Gayral and Mathieu Hoyrup},
journal= {arXiv preprint arXiv:2607.11404},
year = {2026}
}