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

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