The thermodynamics of irreversible processes is based on the expression of the entropy source density derived in the previous chapter. From it, phenomenological laws of transport can be presented in a unified way. Heat transport is given by Fourier’s law that leads to a heat equation in which Joule and Thomson effects can be included. It can explain thermal dephasing, heat exchangers and effusivity. Matter transport leads to the Dufour and Soret effects, which imply Fick’s law and the diffusion equation, which can be used to discuss Turing patterns and ultramicroelectrode. Transport of two types of charge carrier leads to the notion of diffusion length, giant magnetoresistance and planar Ettingshausen effect. Transport can be perpendicular to the generalised force, as in the Hall, Righi-Leduc and Nernst effects. The formalism accounts also for thermoelectric effects such as the Seebeck and Peltier effects, with which to analyse thermocouples, a Seebeck loop, adiabatic thermoelectric junctions, the Harman method of determing the ZT coefficient of a thermoelectric material and the principle of a Peltier generator.

The internal energy of the electromagnetic field is distinct from that of the matter exposed to the field. The choice of field variable is determined by physical considerations concerning the electric, displacement, magnetic and induction fields. Legendre transform are worked out in order to define electric and magnetic enthalpies and free enthalpies. Spatial derivatives of the enthalpies yield the force densities that dielectrics and magnets experience in inhomogeneous electric and magnetic induction fields. Either internal energy or electric enthalpy must be used to analyse the force on a dielectric inserted in a capacitor, depending on the constraint (constant charge or constant field). Likewise, internal energy or magnetic enthalpy must be considered to analyse the force on a paramagnetic material inserted in a coil or in between the poles of a magnet. A complete analysis of adiabatic demagnetisation offers an example of application of Mayer’s relation to specific heat at constant induction field or constant magnetisation. The effect is predicted for the case of a paramagnetic material with a magnetisation that obeys Curie’s law.

By applying the first and second laws to systems consisting of two subsystems separated by a wall, it is possible to determine the equilibrium conditions relevant for that wall's properties, e.g. a fixed diatermal wall, a mobile diathermal wall, a fixed permeable wall. The second law imposes a condition on the entropy production rate which implies relations between heat and temperature difference, matter transfer rate and chemical potential difference, volume rate of change and pressure difference. Thus, transport equations are introducted, akin to Fourier law, Fick law and Poiseuille law. These processes are examples of dissipative processes. A worked solution shows that when two subsystems are subjected to a mechanical action, non-symmetric heat flow may occur.