Theories with Internal Variables

An alternative approach of non-equilibrium thermodynamics may be carried out through the internal variables theory (IVT). This phenomenological description has been very successful in the study of a wide variety of processes in rheology, deformable bodies, physico-chemistry and electromagnetism. IVT may be considered as a generalization of the classical theory of irreversible processes, just like extended irreversible thermodynamics. In the classical theory, the state of the system is described by the local equilibrium variables, say energy, volume or deformation, but it is well known that many non-equilibrium effects cannot be adequately described by this set of variables. To avoid, among others, the inconvenience of a heavy formalism in terms of functionals, one has, in extended irreversible thermodynamics, supplemented the local equilibrium variables by the corresponding fluxes. In the IVT, one adopts a similar attitude by adding a certain number of internal variables to the local equilibrium variables. Such variables are called internal because they are connected either to internal motions or to local microstructures. They should not be confused with order parameters as introduced in Chap. 6, which are describing some broken symmetry related to long-range interactions as in phase transitions. We should also add that unlike the fluxes in extended irreversible thermodynamics, the internal variables are arbitrary extensive quantities, not identified from the outset. It is the freedom in the choice of the internal variables that explains the wide domain of applicability of the formalism.