General Properties of Entropy Production

In the linear regime we saw that the stationary states are those in which the total entropy production P = a dV reaches a minimum. This criterion also assured the stability of the stationary state. In the far-from-equilibrium nonlinear regime there is no such general principle for determining the state of the system. 

Let P be the entropy production in a nonequilibrium stationary state. Since P = y dV = lyY FkJkdV, the rate of change in P can be written as 

In contrast to the variation dG in the Gibbs free energy G, dpP is not a differential of a state function. Hence the fact that dyP can only decrease does not tell us how the state will evolve. 

The first of the above relations follows from the linear relations Jk = Yji kiFi and the Onsager reciprocal relations L = L,vt. First we note that 

Using this result in the definitions of dpP and djP (18.2.1), we immediately see that 

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