One-particle distribution density in the grand canonical ensemble

The grand canonical ensemble of single-component systems of particles in a region is considered. It is shown that if the distribution density of one particle tends to a finite limit as the diameter of tends to infinity then under fairly general conditions this limit is represented by the function that, as is shown in an earlier paper of the author, is, under certain conditions, the analytic continuation of the Mayer expansion representing the density as a function of the activity.All-Russia Correspondence Institute of the Food Industry. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No.1, pp. 44–58, July, 1994.