Symmetrized general hopping current equation

We show that within the validity range of local thermal equilibrium--therein, however, irrespective of the magnitude of the driving force--a simple current equation can be formulated that expresses the current in terms of a product of a local nonequilibrium conductivity and a sinh function of half the electrochemical potential drop (normalized with respect to kBT) over the local hopping distance. This local current/driving force relation takes account of both electrical and compositional effects and can be generalized as to include interactions and structural variations.