Nonequilibrium temperature in the multiscale dynamics and thermodynamics

The basis for defining and measuring temperatures is an equilibration process. In externally unforced systems the equilibration process is the time evolution, driven by entropy, toward the thermodynamic equilibrium states. In the systems subjected to external forces the equilibration process is a time evolution representing the approach from a more detailed level of description to constitutive relations on a less detailed level. This approach is driven by the CR entropy that in the absence of driving forces and after the approach is completed becomes the dissipation potential (a quantity closely related to the entropy production).