AI 中文总结
研究零温度遍历优化中可计算势的最大遍历平均及最大化测度集，在合理假设下证明其为可计算实数与$\Pi_1$可计算紧集，在符号动力学有限型子转移背景下给出有限时间计算两者的显式算法及代码库。
AI 中文摘要
近年来，物理系统与可计算性属性之间的联系一直是一个活跃的研究领域。受先前关于正温度吉布斯测度的工作启发，我们证明在零温度遍历优化的背景下，对于可计算势并在几个合理假设下，最大遍历平均是一个可计算实数，且最大化测度集是一个$\Pi_1$可计算紧集。然后，在符号动力学的更具体背景下，对于有限型子转移上的有限范围相互作用，我们提供了一个显式算法，可在有限时间内计算最大遍历平均和最大化测度集，并配有匹配的代码库。
英文摘要
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.
