There were several cases where I was able to (relatively easily) derive potentials for interactions in my statistical mechanics course. I know that there is no real way to derive the kinetics of a reaction give just the potential difference between the two reactants. However, let's take a look at a specific version of this problem (while leaving it still relatively abstract) with batteries. Construct a simple electrochemical battery starting out with a potential $\varepsilon_0$ at $t_0$ and $\varepsilon_1$at $t_1$.
I was wondering if there was any relationship about the rate of the reactions that you could derive from the ratio of $\varepsilon_0$ to $\varepsilon_1$? (maybe some kind of relative rate)
If not then is there some kind of useful relationship you can define from multiple measurements of $\varepsilon_n$ at $t_n$?
Essentially I'm curious to see if you can make meaningful conclusions about kinetics by combining theoretical models for the potential with experimental data, theoreticla justifications if you will.