A Partition Function Estimator

TL;DR

This paper introduces a straightforward estimator for calculating a system's partition function from finite samples, incorporating a volume correction to improve accuracy, and demonstrates its effectiveness on model systems.

Contribution

The paper presents a novel, simple estimator with a volume correction for accurately computing partition functions from finite samples.

Findings

Estimator achieves excellent agreement with exact solutions

Method effectively accounts for finite sampling limitations

Applicable to various model systems

Abstract

We propose a simple estimator that allows to calculate the absolute value of a system's partition function from a finite sampling of its canonical ensemble. The estimator utilizes a volume correction term to compensate the effect that the finite sampling cannot cover the whole configuration space. As a proof of concept, the estimator is applied to calculate the partition function for several model systems, and the results are compared with the numerically exact solutions. Excellent agreement is found, demonstrating that a solution for an efficient calculation of partition functions is possible.