Entropy determination for mixtures in the adiabatic grand-isobaric ensemble

TL;DR

This paper introduces a Monte Carlo method within an adiabatic grand-isobaric ensemble to rapidly determine the entropy and thermodynamic properties of fluid mixtures, enabling analysis of mixing behavior and deviations from ideality.

Contribution

It generalizes the grand-isobaric ensemble to mixtures and develops a Monte Carlo algorithm for direct entropy calculation in these systems.

Findings

Accurately computes entropy and Gibbs free energy of mixing.

Performs well on simple and complex many-body systems.

Enables efficient detection of non-ideal mixing behavior.

Abstract

The entropy change that occurs upon mixing two fluids has remained an intriguing topic since the dawn of statistical mechanics. In this work, we generalize the grand-isobaric ensemble to mixtures, and develop a Monte Carlo algorithm for the rapid determination of entropy in these systems. A key advantage of adiabatic ensembles is the direct connection they provide with entropy. Here, we show how the entropy of a binary mixture A-B can be readily obtained in the adiabatic grand-isobaric $(\mu_{\text{A}}$, $\mu_{\text{B}}, P, R)$ ensemble, in which $\mu_{\text{A}}$ and $\mu_{\text{B}}$ denote the chemical potential of components A and B, respectively, $P$ is the pressure, and $R$ is the heat (Ray) function, that corresponds to the total energy of the system. This, in turn, allows for the evaluation of the entropy of mixing, as well as of the Gibbs free energy of mixing. We also demonstrate that our approach performs very well both on systems modeled with simple potentials and with complex many-body force fields. Finally, this approach provides a direct route to the determination of the thermodynamic properties of mixing, and allows for the efficient detection of departures from ideal behavior in mixtures.