Two-sided Bogoliubov inequality to estimate finite size effects in quantum molecular simulations

TL;DR

This paper extends the two-sided Bogoliubov inequality to quantum systems, providing bounds on free energy differences to better estimate finite size effects in quantum molecular simulations.

Contribution

It introduces a quantum generalization of the classical Bogoliubov inequality, enabling more accurate finite size corrections in quantum molecular modeling.

Findings

Provides upper and lower bounds for quantum free energy differences.

Applicable to quantum molecular dynamics simulations.

Enhances understanding of finite size effects in quantum systems.

Abstract

We generalise the two-sided Bogoliubov inequality for classical particles from [L. Delle Site et al., J.Stat.Mech.Th.Exp. 083201 (2017)] to systems of quantum particles. As in the classical set-up, the inequality leads to upper and lower bounds for the free energy difference associated with the partitioning of a large system into smaller, independent subsystems. From a thermodynamic modelling point of view, the free energy difference determines the finite size correction needed to consistently treat a small system as a representation of a large system. Applications of the bounds to quantify finite size effects are ubiquitous in physics, chemistry, material science, or biology, to name just a few; in particular it is relevant for molecular dynamics simulations in which a small portion of a system is usually taken as representative of the idealized large system.