Non-equilibrium States

Non-equilibrium thermodynamics provides us with a general framework for the macroscopic description of thermodynamic systems in non-equilibrium states, where the state variables are treated as field variables, i.e., as continuous functions of space coordinates and time. In this field, the balance equation for entropy plays a central role, expressing the fact that the entropy of a volume element changes with time for two reasons. First, it changes because entropy flows into the volume element, and second, because there is an entropy source due to irreversible phenomena inside the volume element. In this chapter, the differential equations for density, momentum, and energy are presented when these thermodynamic variables are considered field variables. An application of the theory is given considering the heating and dissipation processes when a cavity filled with an ideal gas is heated. The chapter ends with the entropy balance equation in its differential and integral forms.