The question arises though, are the irreversible processes constituting time or are they evolving in time? ... What can be said about this?
Two views apparently corresponding to “relationism with respect to time” and “absolutism with respect to time” respectively, (see SEP below). Relationalism is clock time based on the resonant frequency of caesium (or other regular motion); absolutism is the god's eye-view within which caesium clock rates differ depending on local gravity and inertia. Two types of time, complementary and different. However, the absolutist view is a hot topic and widely viewed as bereft of theoretical validity, e.g. "Special relativity eliminates absolute time" - Wikipedia
SEP, Time - 2. Reductionism and Platonism with Respect to Time
Aristotle and Leibniz, among others, have argued that time is not independent of the events that occur in time. This view is typically called either “reductionism with respect to time” or “relationism with respect to time”, since according to this view, all talk that appears to be about time can somehow be reduced to talk about temporal relations among things and events. The opposing view, normally referred to either as “Platonism with respect to time” or “substantivalism with respect to time” or “absolutism with respect to time”, has been defended by Plato, Newton, and others. On this view, time is like an empty container into which things and events may be placed; but it is a container that is independent of what (if anything) is placed in it.