In this paper, we investigate the computability of thermodynamic invariants at zero temperature for one-dimensional subshifts of finite type. In particular, we prove that the residual entropy (i.e., the joint ground state entropy) is an upper semi-computable function on the space of continuous potentials, but it is not computable. Next, we consider locally constant potentials for which the zero-temperature measure is known to exist. We characterize the computability of the zero-temperature measure and its entropy for potentials that are constant on cylinders of a given length k. In particular, we show the existence of an open and dense set of locally constant potentials for which the zero-temperature measure can be computationally identified as an elementary periodic point measure. Finally, we show that our methods do not generalize to treat the case when k is not given

中文翻译：

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零温度下的可计算性

在本文中，我们研究了在零温度下对于有限类型的一维子位移的热力学不变量的可计算性。特别地，我们证明了残差熵（即联合基态熵）是连续势空间上的上半可计算函数，但它是不可计算的。接下来，我们考虑已知存在零温度测量的局部恒定电位。我们描述了零温度测量的可计算性及其熵对于给定长度 k 的圆柱体上恒定的电位。特别是，我们展示了一组开放和密集的局部常数势的存在，零温度测量可以通过计算识别为基本周期点测量。最后，