Nernst equation and electrolysis Let's say we have a stable solution of 
$\mathrm{A}_{\left(\mathrm{aq}\right)}^{2+}$
and $\mathrm{C}_{\left(\mathrm{aq}\right)}^{+}$
, with their respective counter-ions.

The associated redox reactions are:

$\mathrm{A}_{\left(\mathrm{aq}\right)}^{2+}+\mathrm{e}^{-}\rightleftharpoons\mathrm{A}_{\left(\mathrm{aq}\right)}^{+}\qquad\mathcal{E}_{\mathrm{A}_{\left(\mathrm{aq}\right)}^{2+}/\mathrm{A}_{\left(\mathrm{aq}\right)}^{+}}^{\circ}$

$\mathrm{C}_{\left(\mathrm{aq}\right)}^{2+}+\mathrm{e}^{-}\rightleftharpoons\mathrm{C}_{\left(\mathrm{aq}\right)}^{+}\qquad\mathcal{E}_{\mathrm{C}_{\left(\mathrm{aq}\right)}^{2+}/\mathrm{C}_{\left(\mathrm{aq}\right)}^{+}}^{\circ}$

where $\mathcal{E}_{\mathrm{A}_{\left(\mathrm{aq}\right)}^{2+}/\mathrm{A}_{\left(\mathrm{aq}\right)}^{+}}^{\circ}&lt;\mathcal{E}_{\mathrm{C}_{\left(\mathrm{aq}\right)}^{2+}/\mathrm{C}_{\left(\mathrm{aq}\right)}^{+}}^{\circ}$
, since no reaction between $\mathrm{A}_{\left(\mathrm{aq}\right)}^{2+}$
and $\mathrm{C}_{\left(\mathrm{aq}\right)}^{+}$
is occurring. 

The questions are:


Provided that neither $\mathrm{A}_{\left(\mathrm{aq}\right)}^{+}$
nor $\mathrm{C}_{\left(\mathrm{aq}\right)}^{2+}$
are present in the solution, how can we determine, form the Nernst equation, the $\mathcal{E}$ needed to start the electrolysis process 
$\mathrm{A}_{\left(\mathrm{aq}\right)}^{2+}+\mathrm{C}_{\left(\mathrm{aq}\right)}^{+}\rightleftharpoons\mathrm{A}_{\left(\mathrm{aq}\right)}^{ +}+\mathrm{C}_{\left(\mathrm{aq}\right)}^{2+}$?
In other words, how can the Nernst equation deal with activities that are equal to zero?


Thanks in advance!
The Nernst equation only technically applies when the system is in electrochemical equilibrium—when there's no net current flow, but there's actually an exchange current. A system in which the reaction can only happen in one direction because there are no products wouldn't apply. Source:    Electrochemical Dictionary; Bard, A. J.; Inzelt, G.; Scholz, F., Eds.; Springer Berlin Heidelberg: Berlin, Heidelberg, 2008.

What I'm not sure about is the validity of ∆G values calculated from $∆G=∆G°+RT\ln Q$ at the  limits where the system is all products or all reactants. ±∞ don't seem to be meaningful values, but the system should quickly move away from these boundary values, even if only by a small amount. These chemical thermodynamics methods are well-behaved when near equilibrium, but well away from equilibrium, they can produce invalid results.