RESUMEN

We plan to discuss one simple scheme for unification of Quantum dynamics with complex time parameter and non-Hermitian operator of Hamilton. Time, temperature and regime of thermodynamic evolution. Arrow of time in isothermal and adiabatic regimes. Symmetries and conservation lows: fall of the Noeter's theorem. Universal dynamical mechanism of parity violation. Classical limit for generalized quantum dynamics in action-angle variables. Proof of its irreversibility. Classical limit for generalized quantum dynamics in arbitrary canonical variables. Modified Hamilton Jacobi formalism and Hamilton's equations. Classical limit for probability density and dispersion like characteristics. Standard classical dynamics in the limit of delta functional probability density distribution. Proof of the presence of arrow of time in isothermal and adiabatic regimes of classical evolution. Notes about attractor states and chaos in the generalized quantum and classical dynamics developed.