  A novel Einstein relation (fractional Einstein relation, FER) for the
electric conduction in non-crystalline semiconductors is presented. FER and the
generalized Einstein relation (GER) [Phys. Rev. E 8, 1296 (1998)] are compared
to the result of the Monte Carlo (MC) simulation, and is confirmed that FER
exhibits better agreement than GER. The cruial feature of FER is that it
reflects the violation of the detailed balance in the coarse-grained hopping
process, while it is preserved in the original Einstein relation or GER.
