fig4

Figure 4. Schematic of recursive property of entropy in terms of probability tree diagrams with (A) p_x for the ungrouped quantum pure-state configurations (x) without intrinsic entroapy; and (B) $$ p_{k}=\sum_{x} p_{x \mid k} \\ $$ for the grouped intermediate configurations (k) with intrinsic entropy being $$ S_{k}=-k_{B} \sum_{x} p_{x \mid k} \ln \left(p_{x \mid k}\right) \\ $$ where $$ p_{x \mid k} $$ is the conditional probability representing the contribution from configuration x to configuration k.