Short-time nonstationary character of correlation functions in classical equilibrium ensembles

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Abstract
Dynamical quantities b(t) are considered that depend on the canonical variables of a small number n of particles of a classical N-particle condensed system being in thermal equilibrium. It is proved that equalities like d2〈b(0)b(t)〉/dt2=−〈ḃ(0)ḃ(t)〉 are in general violated, if the interparticle interactions have a finite range and sufficiently short times t are considered. This violation reflects the continuous-in-time creations and destructions of s-particle correlations n<s≪N, which are due to the thermal motion.