Thermodynamics generally describes transformations between heat and mechanical work (Planck 1917; Fermi 1956; Schrodinger 1952; Landau and Lifshitz 1958; Reiss 1965; Pauli 1973; Callen 1985). In the present discussion the materials are also mixed at different scales, bringing additional processes into the discussion. As well, for dynamic processes, non-equilibrium thermodynamics needs to be considered (Jammer 1964; Yourgrau et al. 1982; de Groot and Mazer 1984; Haase 1990). For porous materials and other composite media, an important departure in the thermodynamic status of porosity and saturation described in Chapter 4 occurs when irreversible deformations are allowed. In these cases, it is observed that the volume fractions and component velocities are not thermodynamic variables. This is in stark contrast to the previous discussion of equilibrium thermodynamics, where they appeared to be thermodynamic variables. Of course, in hindsight it is observed that they were proportional to the actual thermodynamic variables in the cases considered. In the case of porosity, it is observed that specific mass fractions replace porosity and saturation (volume fractions) as the thermodynamic variables, and a new fundamental quantity appears which is associated with the mass fractions, the order (or structure) of the medium. Of particular importance to non-equilibrium thermodynamics are the modifications momentum flux, etc., make to the Clapeyron equation and the new information about dispersion, porosity waves, fluid flow and their interactions obtained from the new Onsager’s relations.