In problem 2 in Problem Set 6, it is said:
"Electricity prefers to flow in the way that minimizes energy loss to resistance."
Using Lagrange multipliers I was able to show that assuming the above statement, in parallel, $I_kR_k=V$, a constant, for each resistor attached in parallel. Physically, this makes sense since if we assume Ohm's law is obeyed, this result is just an immediate corollary of putting resistors in parallel: the terminals of all the resistors coincide so the potential differences across all the resistors, which are path-independent, are the same.
So my question is, is there a deeper physical reason why current distributes itself so that it minimizes power loss?