Arrow of time, parity violation, and gravity in generalized quantum and classical dynamics

The quantum mechanics with a stationary non-Hermitian Hamiltonian and a complex evolution parameter, as well as its classical limit with nontrivial correlations have been studied. The corresponding dynamics is shown to be irreversible for the isothermal and adiabatic regimes of quantum and classical evolution. The possibility of a universal relationship between irreversibility and dynamical parity violation in the system has been established. The mechanism of gravity generation by the distribution of correlations in a free theory is demonstrated.