Generalized Quantum Dynamics with Arrow of Time
  It is shown, that quantum theory with complex evolutionary time parameter and non-Hermitian Hamiltonian structure can be used for natural unification of quantum and thermodynamic principles. The theory is postulated as analytical in respect to the parameter of evolution, which real part is identified with the `usual' physical time, whereas the imaginary one is understood as proportional to the inverse absolute temperature. Also, the Hermitian part of the Hamiltonian is put equal to conventional operator of energy. It is shown, that the anti-Hermitian Hamiltonian part, which is taken as commuting with the energy operator, is constructed from parameters of decay of the system. It is established, that quantum dynamics, predicted by this theory, is integrable in the same sense as the corresponding non-modified one, and that it possesses a well defined arrow of time in isothermal and adiabatic regimes of the evolution. It is proved, that average value of the decay operator decreases monotonously (as the function of the physical time) in these important thermodynamical regimes for the arbitrary initial data taken. We discuss possible application of the general formalism developed to construction of time-irreversible modification of a string theory. 
Vadim V. Asadov and Oleg V.Kechkin