Thermodynamic Limit in Computer Simulations via Finite-Size Integral Equations

Integral equations (IE) connect the local structure of a liquid with equilibrium thermodynamic quantities such as isothermal compressibility, activity coefficients and excess entropy. IE are usually defined in the grand canonical ensemble and calculated in the thermodynamic limit (TL). By contrast, computer simulations typically consider finite-size systems and mimic the TL using periodic boundary conditions (PBC). This practice introduces various finite-size effects whose effects must be identified and corrected to approximate the simulation results in the TL.

In this talk, we present a generic method to compute IE from molecular dynamics simulations. In our approach, we define finite-size IE, integrating them in Fourier space to trivially introduce PBC. This procedure allows us to isolate ensemble, finite-volume domains and PBC effects and accurately obtain the corresponding thermodynamic quantities in the TL. To validate our method, we compute isothermal compressibilities, chemical potentials and excess entropies of simple liquids and liquid mixtures, including water and aqueous alcohol solutions, showing good agreement with results available in the literature.