The concept underlying Prigogine's ideas is the asymmetric "lifetime" he introduces into thermodynamics in addition to the symmetric time parameter. By identifying processes by means of causal chains of genidentical events, we examine the intrinsic order of lifetime adopting Grunbaum's symmetric time order. Further, we define the physical meaning and the actuality of the processes under consideration. We conclude that Prigogine's microscopic temporal irreversibility is tacitly assumed at macroscopic level. Moreover, his "new" complementarity lacks any scientific foundation. Finally, we put (...) forward the fact-like origin of temporal irreversibility referring to classical thermodynamics. (shrink)