Flux = electrons in the channel ÷ time each one spends there  (Datta Sec. 3.2, Eq. 3.3)

Each box is one state of the channel at energy E. A contact tries to set every box to its own occupation f: an empty box is filled from a contact with probability f, a full box is emptied into it with probability 1 − f, each on a time scale t. Count what flows.