Physical knots observed in various contexts – from DNA biology to vortex dynamics and condensed matter physics – are found to undergo topological simplification through iterated recombination of knot strands following a common, qualitative pattern that bears remarkable similarities across fields. Here, by interpreting evolutionary processes as geodesic flows in a suitably defined knot polynomial space, we show that a new measure of topological complexity allows accurate quantification of the probability of decay pathways by selecting the optimal unlinking pathways. We also show that these optimal pathways are captured by a logarithmic best-fit curve related to the distribution of minimum energy states of tight knots. This preliminary approach shows great potential for establishing new relations between topological simplification pathways and energy cascade processes in nature.

人们发现，在各种情况下（从DNA生物学到涡旋动力学以及凝聚态物理）观察到的物理结，通过按照常见的定性模式对结链进行迭代重组，使结线迭代重组，从而简化了拓扑，并在各个领域具有显着的相似性。在这里，通过将进化过程解释为在适当定义的结多项式空间中的测地线流动，我们表明，拓扑复杂性的新度量允许通过选择最佳解链路径来精确量化衰减路径的概率。我们还表明，这些最佳路径是由与紧密结的最小能量状态分布有关的对数最佳拟合曲线捕获的。