Prolegomena (initial postulates of the approach developed)

• All natural systems are considered as hierarchic systems.

• It is assumed that, at all levels of the system hierarchic structure, there exist substantial flows, and all natural systems are open with respect to these flows. These flows are called generating flows. In particular, our Universe is open to generating flows.

• The union of all sets of elements of a system's generating flows is considered as its space or medium.

• The replacement process (substitution) of generating flow elements in a system is considered as a generalized substitutional motion of the system in its space.

• The sources and drains of the generating flows in the Universe are considered as charges of the existing interactions.

• It is assumed that any variability of natural systems can be described in terms of changing of the set and number of elements of some generating flows in these systems.

• The formation, or the course of time, in systems is considered as changing the amount of substance of some generating flows in these systems.

• For measuring the proper time of a system, it is suggested to count the number of generating flow elements which have been replaced in the system. This is the notion of substitutional, or metabolic clock.

• For structured objects, the notion of the "number of elements" is generalized by using functor invariants of mathematical structures, whose employment leads to the construction of generalized entropy and to the entropy parametrization of time. The use of functor invariants for comparison between structured objects makes it possible to introduce the principle according to which the reality implements the states of systems which possess an extremal structure. It is suggested to use this extremum principle for deriving the equations of substitutional motion.