  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.
