Entropy Production Rate of Non-equilibrium Systems from the Fokker-Planck Equation

The entropy production rate of non-equilibrium systems is studied via the Fokker-Planck equation. This approach, based on the entropy production rate equation given by Schnakenberg from a master equation, requires information on the transition rate of the system under study. We obtain the transition rate from the conditional probability extracted from the Fokker-Planck equation and then derive a new and more operable expression for the entropy production rate. A few examples are presented as applications of our approach.