Finite-size effects of the excess entropy computed from integrating the radial distribution function

Computation of the excess entropy (Formula presented.) from the second-order density expansion of the entropy holds strictly for infinite systems in the limit of small densities. For the reliable and efficient computation of (Formula presented.) it is important to understand finite-size effects. Here, expressions to compute (Formula presented.) and Kirkwood–Buff (KB) integrals by integrating the Radial Distribution Function (RDF) in a finite volume are derived, from which (Formula presented.) and KB integrals in the thermodynamic limit are obtained. The scaling of these integrals with system size is studied. We show that the integrals of (Formula presented.) converge faster than KB integrals. We compute (Formula presented.) from Monte Carlo simulations using the Wang–Ramírez–Dobnikar–Frenkel pair interaction potential by thermodynamic integration and by integration of the RDF. We show that (Formula presented.) computed by integrating the RDF is identical to that of (Formula presented.) computed from thermodynamic integration at low densities, provided the RDF is extrapolated to the thermodynamic limit. At higher densities, differences up to (Formula presented.) are observed.