Thermodynamic Evolution Equation for a Quantum Statistical Gas

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Abstract
It is shown by a perturbation diagram method that partial Green's functions satisfy closed evolution equations exact in the thermodynamic limit except for the neglect of the contribution of initial particle correlations. This contribution is negligible for a system at a time t ≫ τc (average collision duration) when the main interaction processes are localized in space and time. In particular this makes unnecessary the often imposed assumption of the absence of initial particle correlations for the derivation of the usual Boltzmann equation or its generalizations.