Calculations of canonical averages from the grand canonical ensemble

TL;DR

This paper introduces a method to accurately compute canonical ensemble averages using grand canonical ensemble calculations, facilitating easier analysis of finite systems where ensemble equivalence does not hold.

Contribution

The paper presents a novel approach to derive canonical averages from grand canonical ensemble calculations, addressing finite-size effects.

Findings

Enables calculation of canonical averages from grand canonical data

Improves accuracy for finite systems where ensembles differ

Simplifies computational procedures for canonical ensemble analysis

Abstract

Grand canonical and canonical ensembles become equivalent in the thermodynamic limit, but when the system size is finite the results obtained in the two ensembles deviate from each other. In many important cases, the canonical ensemble provides an appropriate physical description but it is often much easier to perform the calculations in the corresponding grand canonical ensemble. We present a method to compute averages in canonical ensemble based on calculations of the expectation values in grand canonical ensemble. The number of particles, which is fixed in the canonical ensemble, is not necessarily the same as the average number of particles in the grand canonical ensemble.