Abstract
Three non-equilibrium equations have been derived describing the evolution of the matrix elements, which are highly off-diagonal on the internal energy of the singlet density operator, ϱ(1), of a quantum dilute gas of molecules with internal levels. The first equation has been obtained by assuming the requirement of sufficient spacing of the spectral transition lines, the second one being its extension for weakly inhomogeneous gases and the third one the equation generalized for spectral transition lines of arbitrary spacing. They have been obtained inside the framework of the subdynamics theory of the Brussels Group where the Π-subdynamics have been explicitly constructed.
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