Unbiased estimators for spatial distribution functions of classical fluids

TL;DR

This paper introduces unbiased estimators for spatial distribution functions in classical fluids, improving accuracy over traditional methods by leveraging a statistical-mechanical identity related to the virial theorem.

Contribution

It derives novel unbiased estimators for fluid density and pair correlation functions, demonstrated through numerical examples showing advantages over histogram-based approaches.

Findings

Estimators provide more accurate distribution functions.

Numerical examples confirm advantages over traditional methods.

Applicable to classical fluid systems.

Abstract

We use a statistical-mechanical identity closely related to the familiar virial theorem, to derive unbiased estimators for spatial distribution functions of classical fluids. In particular, we obtain estimators for both the fluid density rho(r) in the vicinity of a fixed solute, and for the pair correlation g(r) of a homogeneous classical fluid. We illustrate the utility of our estimators with numerical examples, which reveal advantages over traditional histogram-based methods of computing such distributions.