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→因果涌现的最优化
<math>
<math>
\Delta\mathcal{J}_2=\ln\frac{|\det(A)|^\frac{1}{n}}{|\det(WAW^\dagger)|^\frac{1}{k}}\geq\ln\frac{|\prod_{i=1}^n|^\frac{1}{n}}{|\prod_{i=1}^k|^\frac{1}{k}}\geq-\frac{1}{k}\sum_{i=1}^{k}\ln\displaystyle|\lambda_i|+\frac{1}{n}\sum_{i=1}^{n}\ln\displaystyle|\lambda_i|
\Delta\mathcal{J}_2=\ln\frac{|\det(A)|^\frac{1}{n}}{|\det(WAW^\dagger)|^\frac{1}{k}}\geq\ln\frac{|\prod_{i=1}^n\lambda_i|^\frac{1}{n}}{|\prod_{i=1}^k\lambda_i|^\frac{1}{k}}=-\frac{1}{k}\sum_{i=1}^{k}\ln\displaystyle|\lambda_i|+\frac{1}{n}\sum_{i=1}^{n}\ln\displaystyle|\lambda_i|
</math>
因果涌现最大值为
<math>
\Delta\mathcal{J}^{*}=\frac{1}{k}\sum_{i=1}^{k}\ln\displaystyle|\lambda_i|-\frac{1}{n}\sum_{i=1}^{n}\ln\displaystyle|\lambda_i|+\eta
</math>
</math>