On the existence of functionals for the mean values of observables

TL;DR

This paper investigates the conditions under which mean values of observables exist for infinite-particle systems, focusing on solutions to the BBGKY hierarchy and their duals, with results on local in time existence.

Contribution

It establishes the local in time existence of mean value functionals for infinite-particle systems using solutions to the BBGKY hierarchy and explores conditions for various classes of observables.

Findings

Proved local in time existence of mean value functionals.

Analyzed existence conditions for different classes of observables.

Discussed extension to arbitrary time intervals.

Abstract

The aim of this work is to study the existence of mean values of observables for infinite-particle systems. Using solutions of the initial value problems to the BBGKY hierarchy and to its dual, we prove the local, in time, existence of the mean value functionals in the cases where either observables or states vary in time. We also discuss problems on the existence of such functionals for several different classes of observables and for an arbitrary time interval.