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Uncertainty is an important feature of dynamic systems, and entropy has beenwidely used to measure this attribute. In this Letter, we prove that stateaggregation and decomposition can decrease and increase the entropy,respectively, of dynamic systems. More than 20 popular entropies in theliterature are summarized and analyzed, and it is noted that none of thembreaks this property. Finally, pertinent proofs are given for four cases.

On Uncertainty of Dynamic Systems via State Aggregation Coarse-Graining and State Decomposition Fine-Graining Ways