Physical Review Research (May 2022)

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

  • Akira Yoshida,
  • Naoko Nakagawa

DOI
https://doi.org/10.1103/PhysRevResearch.4.023119
Journal volume & issue
Vol. 4, no. 2
p. 023119

Abstract

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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.