Irreversible Thermodynamics and the Generalized Ficks Law

We leave it as an exercise for our readers to calculate the eigenvalues of [P ]. These values should be equal to the eigenvalues of [ ].  

Support for the form of the generalized Fick s law of the preceding section can be found in irreversible thermodynamics introduced in Section 2.3. The treatment below follows that of Stewart and Prober (1964), but readers will also find the books by de Groot and Mazur (1962) and Haase (1969), and the review of Kirkaldy (1970) very useful. 

The starting point for our analysis is an expression for the rate of entropy production per unit volume. For isothermal, isobaric processes in the absence of external force fields, the rate of entropy production due to ditfusion is given by (cf. Eq. 2.3.1) 

At equilibrium both the fluxes and the driving forces vanish simultaneously giving 

We now postulate a linear relationship between independent fluxes and driving forces 

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