On the time-dependent formulation of analytical continuation in non-equilibrium statistical mechanics

On the basis of the dynamics-of-correlations approach to the solution of the Liouville-von Neumann equation, we develop within the familiar classification of correlations scheme a time-dependent formalism which leads naturally to an analytical continuation procedure, thereby allowing explicit evaluation of each term in the formal series solution. This procedure throws new light on the so-called iϵ-rule, and opens the way to the treatment of the full correlation subdynamics for time-dependent phenomena, which will be discussed in future publications.