May the dU/dx be with you

Geometry Rescaling
One of the major issues with the stability of the timemachine is whether or not your Hessians are PSD. A nonPSD Hessian induces a transition matrix with a spectral radius , causing a divergent trajectory. Recall Brownian dynamics: Assuming a zero mixed partial, we can differentiate with respect to G and H are the Gradients… Read more

Derivatives and Internal Coordinates
Brownian Dynamics has the following equations of motion, where we assume that the geometries is dependent on the forcefield parameters We can differentiate the above w.r.t. For the purposes of stability analysis and without loss of generality we can assume: So we can proceed to simplify into: It can be shown that this converges if… Read more
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