\Delta\mathcal{J}=\mathop{\ln\frac{|\det(WAW^\dagger)|^\frac{1}{k}}{|\det(A)|^\frac{1}{n}}}_{Degeneracy Emergence}-\mathop{\ln\frac{|\det(W\Sigma W^{T})|^\frac{1}{2k}}{|\det(\Sigma)|^\frac{1}{2n}}}_{Determinism Emergence} | \Delta\mathcal{J}=\mathop{\ln\frac{|\det(WAW^\dagger)|^\frac{1}{k}}{|\det(A)|^\frac{1}{n}}}_{Degeneracy Emergence}-\mathop{\ln\frac{|\det(W\Sigma W^{T})|^\frac{1}{2k}}{|\det(\Sigma)|^\frac{1}{2n}}}_{Determinism Emergence} |