Work relation for determining the mixing free energy of small-scale mixtures

TL;DR

This paper develops a new work relation for calculating the mixing free energy of small molecular mixtures, bypassing traditional membrane-based methods, and demonstrates its application to argon-krypton mixtures.

Contribution

It introduces a novel work relation for mixing free energy that does not require semipermeable membranes, enhancing thermodynamic analysis of small mixtures.

Findings

Numerical validation with argon-krypton mixture.

The mixing free energy reflects liquid-vapor transition characteristics.

Comparison reveals a combinatorial factor related to molecule indistinguishability.

Abstract

In thermodynamically characterizing a mixture comprising a finite number of molecules, we consider two kinds of protocol for producing a mixture from a pure substance. The first is a single alchemical operation, whereas the second is a series of processes with feedback control in information thermodynamics and conventional mixing with semipermeable membranes. A comparison of the two numerically determined free-energy changes provides a combinatorial factor that indicates the indistinguishability of the molecules and an alternative Jarzynski equality. The comparison also uncovers a work relation for determining the mixing free energy without using semipermeable membranes. We demonstrate a numerical calculation of applying the work relation to a mixture of argon and krypton. The mixing free energy clearly shows the characteristics of liquid--vapor transition.