Assuming that you have ideal ohmic contacts connecting the metal and the conductor, the only "source" of voltage drop in the system is the contacts. Think about the 1D Poisson's equation. It is second-order, and requires two boundary conditions to solve. One condition just sets the potential...
I've been refreshing myself on some of the statistical mechanics I learned a couple years ago, using Kittel and Kroemer as a guide. However, I've come across a couple things that bother me:
1. When the Boltzmann distribution is derived, no real physics enters the picture. Essentially, the...