  We present a new perturbative formulation of non-equilibrium thermal field
theory, based upon non-homogeneous free propagators and time-dependent
vertices. The resulting time-dependent diagrammatic perturbation series are
free of pinch singularities without the need for quasi-particle approximation
or effective resummation of finite widths. After arriving at a physically
meaningful definition of particle number densities, we derive master time
evolution equations for statistical distribution functions, which are valid to
all orders in perturbation theory and all orders in a gradient expansion. For a
scalar model, we make a loopwise truncation of these evolution equations,
whilst still capturing fast transient behaviour, which is found to be dominated
by energy-violating processes, leading to non-Markovian evolution of memory
effects.
