It is shown that the evolution processes of any part or degree of freedom of an isolated heterogeneous system are carried out by performing work on them against the balance of other parts or degrees of its freedom and are accompanied by their involution. This unity of the processes of evolution and involution makes the thermodynamic criteria of the one-sided directionality of spontaneous processes unacceptable for them and requires an explicit consideration of their opposite orientation with the help of specific nonequilibrium parameters. Parameters characterizing the removal from internal equilibrium of any macrosystems up to the Universe as a whole are introduced, and on their basis the criteria of evolution and involution of systems for each degree of freedom inherent in them are proposed. These criteria confirm the presence in nature not only destructive, but also creative tendencies. The sources of free energy of the Universe caused by the processes of wave formation in a non-baryonic substance and responsible for the evolution processes in all its subsystems of any hierarchical level and any (organic and inorganic) origin are revealed. Examples of evolutionary processes in the observable (baryonic) matter of the Universe that support these criteria are given. The conclusion is made that the concepts of "the emergence of order from chaos", "self-organization" of closed systems as a whole, "time arrows" and "thermal death" of the Universe are groundless.