Extremum Principles Predict Equilibria

Irreversible processes may promote disorder at near equilibrium, and promote order at far from equilibrium known as the nonlinear region. For systems at far from global equilibrium, flows are no longer linear functions of the forces, and there are no general extremum principles to predict the final state. Chemical reactions may reach the nonlinear region easily, since the affinities of such systems are in the range of 10-100 kJ/mol. However, transport processes mainly take place in the linear region of the thermodynamic branch. 

Equations (7.4) and (7.5) are completely general statements that there are some functional dependences S U, V,N) and U(S, V, N), and that these dependences define T, p, and p. Equations (7.4) and (7.5) are fundamental because they completely specify all the changes that can occur in a simple thermodynamic system, and they are the bases for extremum principles that predict states of equilibria. An important difference between these fundamental equations and others that we will write later is that S and U are functions of only the extensiv e variables. Beginning on page 111 we will show how to use Equations (7.4) and (7.5) to identify states of equilibrium. 

---