− | \Delta \mathcal{J}\equiv \mathcal{J_F}-\mathcal{J_f}=\frac{\mathcal{EI_F}}{N}-\frac{\mathcal{EI_f}}{n}\approx \frac{N}{n}\int_{-\frac{L}{2}}^{\frac{L}{2}}\ln\frac{\left|\det\left(\frac{\partial_\mathbf{x} f(\mathbf{x})}{\Sigma^{1/2}}\right)\right|^2}{\left|\det\left(\frac{\partial_\mathbf{X} F(\mathbf{X})}{\Sigma_N^{1/2}}\right)\right|^2} d\mathbf{x} | + | \Delta \mathcal{J}\equiv \mathcal{J_F}-\mathcal{J_f}=\frac{EI_F}{N}-\frac{EI_f}{n}\approx \frac{N}{n}\int_{-\frac{L}{2}}^{\frac{L}{2}}\ln\frac{\left|\det\left(\frac{\partial_\mathbf{x} f(\mathbf{x})}{\Sigma^{1/2}}\right)\right|^2}{\left|\det\left(\frac{\partial_\mathbf{X} F(\mathbf{X})}{\Sigma_N^{1/2}}\right)\right|^2} d\mathbf{x} |