We find a process that violates the principle of least potential energy. It is shown in the figure. How is the entropy of mixing of the solution and the entropy change of the system in this process calculated?
Assuming this process actually happens, the main contribution to entropy would be the dilution:
https://chem.libretexts.org/Bookshelves/General_Chemistry/Chem1_(Lower)/15%3A_Thermodynamics_of_Chemical_Equilibria/15.05%3A_Thermodynamics_of_Mixing_and_Dilution
But I doubt that this process will take such a simple route if you do not apply an external force like a temperature gradient (and then the least energy principle is reestablished). The dilution entropy would have to be so large that it presses the Helmholtz Free energy (whose minimization is the actual requirement under these conditions) for the entire redistribution process below 0.
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