We prove that given a computable metric space and two computable measures, the set of points that have high universal uniform test scores with respect to the first measure will have a lower bound with respect to the second measure. This result is transferred to thermodynamics, showing that algorithmic thermodynamic entropy must oscillate in the presence of dynamics. Another application is that outliers will become emergent in computable dynamics of computable metric spaces.

翻译：我们证明，在给定可计算度量空间和两个可计算测度的情况下，关于第一个测度具有高通用统一检验得分的点集，其关于第二个测度的下界存在。该结果被推广至热力学领域，表明算法热力学熵在存在动力学作用时必然发生振荡。另一个应用是：在可计算度量空间的可计算动力学过程中，异常点将涌现。