Abstract: Conductivity is a measurement of the strength of the conductive ability.It is known that the conductivity of the ionic conduction can be obtained by calculating the average drift velocity of the ion.We present here a new derivation by using entropy.We identify a competition between the system entropy and the environment entropy.The entropy competition determines the most probability electric current from whose form the same conductivity is extracted.Finally,we compare the methods based on entropy and drift velocity and generalize this method to general conductor.This method may be extend to study other conductors.

Key words: ion conductor, conductivity, maximum entropy principle, non-equilibrium state