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First of all, <ref name="Eberhardt"/> points out that if there are no constraints on the coarse-graining scheme, ambiguity may arise when coarse-graining the transition probability matrix (TPM) (merging states and adding up probabilities). For example, when the two row vectors in the TPM corresponding to the two states to be merged are very dissimilar, forcibly merging them (for example, by taking the average) will cause ambiguity. This ambiguity is mainly manifested in the question of what exactly the intervention on the merged macroscopic state means. Since the row vectors are dissimilar, the intervention on the merged macroscopic state cannot be simply reduced to the intervention on the microscopic states. If the intervention on the macroscopic state is forcibly converted into the intervention on the microscopic states by taking the average, the differences between the microscopic states are ignored. At the same time, new contradictory problems of non-commutativity will also be triggered.
First of all, <ref name="Eberhardt"/> points out that if there are no constraints on the coarse-graining scheme, ambiguity may arise when coarse-graining the transition probability matrix (TPM) (merging states and adding up probabilities). For example, when the two row vectors in the TPM corresponding to the two states to be merged are very dissimilar, forcibly merging them (for example, by taking the average) will cause ambiguity. This ambiguity is mainly manifested in the question of what exactly the intervention on the merged macroscopic state means? Since the row vectors are dissimilar, the intervention on the merged macroscopic state cannot be simply reduced to the intervention on the microscopic states. If the intervention on the macroscopic state is forcibly converted into the intervention on the microscopic states by taking the average, the differences between the microscopic states are ignored. At the same time, new contradictory problems of non-commutativity will also be triggered.
====Non-commutativity====
====Non-commutativity====