Implicit dependence of reaction rate through reduction potential and activation energy
The rate of a reaction depends on the thermodynamics of its transition state.
It would be better to look at it in terms of Gibbs activation energy. Therefore there two factors affecting the rate of a reaction:


the activation enthalpy $\Delta^‡ H $, that corresponds to the Arrhenius activation energy
the activation entropy $\Delta^‡ S $ that takes into account the probability of a transition state.


The whole dependency of the kinetic constant on these parameters is expressed by the Eyring and Wynne-Jones equation:
$$ k = \frac{k_\text{B}T}h \operatorname{e}^{\frac {\Delta^‡ S} R }\operatorname{e}^{-\frac{\Delta^‡ H} {RT} }$$

Where $T$ is the temperature, $k_\text{B}$ is the Boltzman constant and $h$ is the Planck constant.
Sometimes a reflection coefficient $\kappa$ is added to the equation to take into account some other dependencies. It is near to 1 for most of the simple reactions.
$$ k = \kappa \frac{k_\text{B}T}h \operatorname{e}^{\frac {\Delta^‡ S} R }\operatorname{e}^{-\frac{\Delta^‡ H} {RT} }$$