Irreversible processes and temperature

The notion of nonequilibrium temperature used in extended irreversible thermodynamics (EIT) is examined from the viewpoints of thermodynamic laws and statistical mechanics in this article. It is shown that in both the phenomenological theory and statistical mechanics of irreversible processes the notion of nonequilibrium temperature in some versions of EIT inevitably came about since a nonequilibrium entropy was not derived from the thermodynamic laws but was arbitrarily assumed and consequently not given its thermodynamic foundations. It is also shown that there is no other temperature than the one established by the zeroth law of thermodynamics and based on the second law of thermodynamics, regardless of whether the system is in equilibrium or nonequilibrium. When such a notion breaks down because the temporal evolution of dynamical processes is faster than the time scale of thermometric resolution, the thermodynamics of irreversible processes (e.g., EIT) is no longer applicable.