Why is chemical potential equivalent to a true potential? My K&K thermal physics testbook says chemical potential is equivalent to a true potential:

the chemical potential is equivalent to a true potential energy: the difference in chemical potential between two systems is equal to the potential barrier that will bring the two systems into diffusive equilibrium.

However, I am very confused - since there is no conservative force generally, how come it is "equivalent" to a true potential? 
We say "two are equivalent", usually when there is no experimental way to distinguish one from another. But surely there is: putting a test charge. Or is the book just saying effectively/phenomenologically their numerical values are equal? What exactly meant by saying these two are equivalent in the text?

I've checked Wiki: "Helmholtz free energy is the Legendre transformation of internal energy"; hence, Chemical potential is the change in Helmholtz free energy (some redefinition of internal energy) when we remove/add some particles. Given some conditions (e.g.two systems are connected), chemical potential (no conservative field at all, I think?) is equivalent to a real potential (with conservative field). 
But I am not very certain if I do not misunderstand anything.
 A: Chemical potential is the difference in free energy to add a particle to the system. Consider two systems (1,2) with a contact with the reservoir at temperature $T$, then total free energy is
\begin{equation}
G = G_{1}+G_{2}
\end{equation}
But since the total number of particles is conserved
\begin{equation}
N = N_{1}+N_{2}
\end{equation}
Heltmholtz free energy will be minimum at equilibrium with respect to
$dN_{1}= -dN_{2}$. Then,
\begin{equation}
\frac{\partial G}{\partial N} = \frac{\partial G_{1}}{\partial N_{1}}_{T,V}+\frac{\partial G_{2}}{\partial N_{2}}_{T,V} = 0.
\end{equation}
That means their chemical potential is same when there is no net particle exchange since
\begin{equation}
\mu_{1} = \mu_{2} \equiv \frac{\partial G_{1}}{\partial N_{1}}_{T,V} = \frac{\partial G_{2}}{\partial N_{2}}_{T,V}
\end{equation}
since $dN_{1}= -dN_{2}$. Therefore, chemical potential difference should indicate particle flow between two systems right? After all, when the difference is zero no net particle flows between them.
Now consider two systems with a different chemical potential. $\mu_{2}>\mu_{1}$ and temporarily block the diffusion between them. Now introduce a field between two systems so that system 1 particles have higher potential energy by an amount of $\delta\mu = \mu_{2}-\mu_{1}$. Therefore, we have basically increased the internal energy of the system 1, $U_{1}$ by  $\delta\mu$ amount right?.
Now, by our previous argument if we carry out the free energy calculation,$G = U-TS+PV$ stuff, we will find out their chemical potential would be same. That means even if we remove the blockage no net particle will flow. Therefore, do we achieve direct translation of potential energy difference with the chemical potential difference?
