  Non-equilibrium processes in Schottky systems generate by projection onto the
equilibrium subspace reversible accompanying processes for which the
non-equilibrium variables are functions of the equilibrium ones. The embedding
theorem which guarantees the compatibility of the accompanying processes with
the non-equilibrium entropy is proved. The non-equilibrium entropy is defined
as a state function on the non-equilibrium state space containing the contact
temperature as a non-equilibrium variable. If the entropy production does not
depend on the internal energy, the contact temperature changes into the
thermostatic temperature also in non-equilibrium, a fact which allows to use
temperature as a primitive concept in non-equilibrium. The dissipation
inequality is revisited, and an efficiency of generalized cyclic processes
beyond the Carnot process is achieved.
