I'm trying to learn a bit about non-equilibrium thermodynamics, and am currently reading de Groot and Mazur. In it, there is a quote right in the beginning, talking about the phenomenological equations, such as Fick's law and Fourier's law, being linear:
Non-equilibrium thermodynamics, in its present form, in mainly restricted to the study of such linear phenomena. Very little of a sufficiently general nature is known outside this linear domain. This is not a very serious restriction however, since even in rather extreme physical situations, transport processes, for example, are still described by linear laws.
I can think of several examples that seem nonlinear to me, e.g. materials where the thermal conductivity depends on the temperature, or the magnetic permeability of ferromagnetic materials.
Are these cases simply not covered by this theory (in which case I would consider this quite a serious restriction), or do I misunderstand a) what they mean by "linear" or b) something else?