On the law of increasing entropy and the cause of the dynamics irreversibility of quantum systems

It has been shown that time reversal symmetry breaking in the dynamics of large systems originates from symmetry breaking in the occupation of the Hilbert space. The states $\phi$, for which the entropy of the system (sub-system) increases, are automatically created in nature or can be prepared experimentally, in contrast to the respective complex-conjugate states ($\phi^*$), for which the entropy decreases (although formally, according to the superposition principle, they can exist). It is indicated that, in the general case, the dynamics reversal of unknown states is impossible because the complex conjugation operator is antilinear. The complexity of reversal of the known state is exponential in the typical case of a large system. The formulated statements are illustrated by simple models.