Consider a rigid, adiabatic, impermeable cylinder (i.e., a closed isolated system) that consists of two chambers (i.e., simple systems) that are separated by a wall that is permeable, immovable, and diathermal. Suppose that initially, the fluids in the two chambers are at the same temperature, T, but have different chemical potentials with ?2 > ?1. Following our earlier arguments considering entropy changes for heat transfer, demonstrate that a. the fluid will flow from chamber 2 into chamber 1, and b. this flow will continue until the two fluids are at the same chemical potential.