1 What Can Non-Equilibrium Thermodynamics Offer?

Non-equilibrium thermodynamics (NET) offers a systematic way to derive the local entropy production rate, ?, of a system. The total entropy production rate is the integral of the local entropy production rate over the volume, V, of the system, but, in a stationary state, it is also equal to the entropy flux out, J _s ⁰, minus the entropy flux into the system, J _s ⁱ:

The entropy flux difference and the integral over ? can be calculated independently, and they must give the same answer. The entropy production rate governs the transport processes that take place in the system. We have

where J _i and X _i are conjugate flux-force pairs. Each flux is a linear combination of all forces:

This means that NET gives flux equations in agreement with the second law of thermodynamics, and that the theory offers a possibility, through Equation (1), to check for consistency in the models that are used.

The usefulness of NET in describing industrial problems has been questioned, because these problems are frequently non-linear. It is then important to know that the flux-force relations in Equation (3) also describe non-linear phenomena. The phenomenological coefficients L _ij can, for instance, be functions of the state variables. By including internal variables in the thermodynamic description, one can extend the application of NET to activated processes; see Chapter 2. For this reason, NET appears...