Direct access to thermodynamics from equilibrium compositional heterogeneities

Abstract

Equilibrium compositional heterogeneities contain thermodynamic information that is typically accessed through multiple bulk states. Here, we show that this information can be extracted from a single system, providing access to thermodynamic properties over a broad range of local compositions. In practice, a single equilibrium simulation is sufficient to recover this behavior. In the system considered here, the excess chemical potential of water follows a simple and thermodynamically consistent dependence on local composition, enabling the recovery of the concentration-dependent extraction behavior across extractant concentrations from a single liquid–liquid system. Within the present framework, this approach provides access to equilibrium distributions across compositions from a single system. The resulting relationship quantitatively reproduces experimental data and retains predictive power well beyond the range over which it is established. Remarkably, the same functional dependence is recovered from local compositional variations in homogeneous systems, indicating that it suggests an intrinsic thermodynamic property rather than a feature specific to interfacial environments. The corresponding response coefficient suggests a possible connection with correlation-based statistical mechanical descriptions such as Kirkwood–Buff-type approaches. Altogether, these results show that compositional heterogeneities can be used as a thermodynamic sampling approach, enabling access to thermodynamic properties without sampling multiple bulk states or explicitly computing intermolecular correlation functions. Because this approach relies solely on equilibrium local composition variations, it is not restricted to molecular simulations and can, in principle, be extended to experimental measurements of local composition.