Key Equations
TRVIT Theorem 3.1:
$$\Phi(t_0,\tau) = \frac{|\sum_\alpha w_\alpha I_C(\alpha, t_0, \tau)|}{I_E(t_0, \tau) \cdot \sum_\alpha w_\alpha}$$
Energy Decay:
$$I_E(t_0,\tau) = \frac{e^{-\gamma t_0} - e^{-\gamma(t_0+\tau)}}{\gamma\tau}$$
Hamiltonian:
$$H = \sum \frac{p^2}{2m} + \frac{1}{2}\sum k_{ij}(q_i-q_j)^2$$
Virial (Clausius 1870):
$$\langle T \rangle = -\frac{1}{2}\langle \sum r_i \cdot F_i \rangle$$
GOMT Scalar:
$$\Omega = \frac{\sum_\alpha \omega_\alpha \cdot w_\alpha}{\sum w_\alpha}$$