标题： 因果涌现的原因：不确定性再分配及其临界条件 显示英文标题

标题： Cause of Causal Emergence: Redistribution of Uncertainty and Its Critical Condition

摘要： 在构建复杂系统的有效且信息丰富的表示时，选择适当的尺度至关重要。 科学家们精心选择实验的尺度，以提取描述系统因果关系的变量。 他们发现，粗尺度（宏观）有时比大量参数观测（微观）更具因果性和信息量。 通过粗粒化出现因果关系的现象称为因果涌现（CE）。 基于信息论，近年来的一些工作已经定量地证明，在将微观模型粗粒化到宏观时，CE确实会发生。 然而，现有的工作并未讨论CE发生的原因和条件。 我们对粗粒化过程中不确定性的重新分布进行了定量分析，并提出不确定性的重新分布是因果涌现的原因。 我们进一步分析了决定CE是否发生的关键阈值。 从离散系统的转移概率矩阵（TPM）的规律性中，推导出模型属性的数学表达式。 计算了不同操作的阈值数值。 结果提供了CE的关键和具体条件，为选择适当的粗粒化操作提供了有益的建议。 结果还提供了一种新的方法来更好地理解因果性和因果涌现的本质。 显示英文摘要

摘要： It is crucial to choose the appropriate scale in order to build an effective and informative representation of a complex system. Scientists carefully choose the scales for their experiments to extract the variables that describe the causalities in the system. They have found that the coarse scale(macro) is sometimes more causal and informative than the numerous-parameter observations(micro). The phenomenon that the causality emerges by coarse-graining is called Causal Emergence(CE). Based on information theory, a number of recent works have quantitatively shown that CE indeed occurs while coarse-graining a micro model to the macro. However, the existing works have not discussed the question of why and when the CE occurs. We quantitatively analyze the redistribution of uncertainties for coarse-graining and suggest that the redistribution of uncertainties is the cause of causal emergence. We further analyze the thresholds that determine if CE occurs or not. From the regularity of the transition probability matrix(TPM) of discrete systems, the mathematical expressions of the model properties are derived. The values of thresholds for different operations are computed. The results provide the critical and specific conditions of CE as helpful suggestions for choosing the proper coarse-graining operation. The results also provide a new way to better understand the nature of causality and causal emergence.