Hi, I'm currently studying in an introductory semiconductor course where we use the following equations (numbers 1-5 on the first page): http://web.mit.edu/kimt/www/6.012/TheFiveEquations.pdf as a model of the underlying physics. Now, it is claimed that at thermal equilibrium, we can take J_e and J_h to be identically zero. As I understand it, the requirement of T.E. allows us to state that the derivatives w.r.t. time are zero. However, I'm not certain as to why we need to mandate that the currents are zero. Of course there's the intuitive notion that if there are currents, then things are moving and thus are not "at equilibrium"; but what I'm looking for is an algebraic derivation from the physical equations that restrict the current to be zero. However, I have not had too much success so far, and most resources just seem to assume that J_i = 0 at thermal equilibrium as a trivial result. Can anyone give me some suggestions on how to begin?