Conventional thermodynamics is a static theory about systems that are in a state of stable equilibrium, establishing the relations among the variables that describe these equilibrium states. Therefore, the dynamic insight comes in two forms: (1) knowing the initial and final equilibrium states, one can authoritatively say whether such transformation can take place spontaneously or not; (2) if the change from an initial to a final state is so slow that the process can be assumed to be proceeding through a series of closely spaced equilibrium states, then such a process is called reversible and the entire path of time evolution of each of the state variables can be obtained from conventional thermodynamics. On the other hand, almost all the processes that we experience are irreversible and hence, most of the time, systems are not in a state of equilibrium as they evolve in time. A very simple and relevant example is that of thermal conduction, when a heat flux is induced by an imposed temperature difference, trying to re-establish the condition of thermal equilibrium, with uniform temperature. Obviously, the word “temperature” here does not indicate exactly a thermodynamic quantity, as it refers to a system that is out of equilibrium. Accordingly, we must extend the meaning of temperature, defining it locally, i.e. within a small volume and a short time interval, so that it can be defined in terms its mean value, neglecting all fluctuations.