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

Akira Yoshida; Naoko Nakagawa

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arXiv · 2111.06110

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

Akira Yoshida·Naoko Nakagawa

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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.

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Akira Yoshida, Naoko Nakagawa. 2021-11-11. Work relation for determining the mixing free energy of small-scale mixtures. https://arxiv.org/abs/2111.06110

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