I asked about the effect of pressure on a reaction, and since then I learned a lot more. One of the things I learned was the Eyring equation:
$$\kappa = \frac{\kappa_B T}{h} e^\frac{\Delta^\ddagger S°}{R} e^\frac{- \Delta^\ddagger H°}{R}$$
where:
$\begin{multline} \begin{split} \kappa &= \text{reaction rate} \\ \kappa_B &= \text{Boltzmann constant} \\ T &= \text{temperature} \\ h &= \text{Planck's constant} \\ R &= \text{gas constant} \\ \Delta^\ddagger S° &= \text{entropy of activation} \\ \Delta^\ddagger H° &= \text{enthalpy of activation} \\ \end{split} \end{multline}$
My questions:
Is the enthalpy of activation the same thing as the activation energy?
Is there a purely mathematical way to determine both $\Delta^\ddagger S°$ and $\Delta^\ddagger H°$? (without having a laboratory to use to observe the reaction)