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We generalise the two-sided Bogoliubov inequality for classical particlesfrom [L. Delle Site et al., J.Stat.Mech.Th.Exp. 083201 (2017)] to systems ofquantum particles. As in the classical set-up, the inequality leads to upperand lower bounds for the free energy difference associated with thepartitioning of a large system into smaller, independent subsystems. From athermodynamic modelling point of view, the free energy difference determinesthe finite size correction needed to consistently treat a small system as arepresentation of a large system. Applications of the bounds to quantify finitesize effects are ubiquitous in physics, chemistry, material science, orbiology, to name just a few; in particular it is relevant for moleculardynamics simulations in which a small portion of a system is usually taken asrepresentative of the idealized large system.

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