零温可计算性

摘要：

本文研究了一维有限型子位移的零温热力学不变量的可计算性。特别是，我们证明了剩余熵（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，我们考虑局部恒定的潜力，零温度措施是已知存在的。我们的零温度措施和熵的潜力是恒定的圆柱体上的一个给定的长度k的可计算性的特点。特别是，我们表明存在一个开放的和密集的一组局部恒定的潜力，零温度措施可以计算确定为一个基本的周期点措施。最后，我们表明，我们的方法不推广到处理的情况下，k是不给

英文摘要：

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

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