You grow a million cells, half of which are liver cells and half of which are vascular cells, on the surface of a Petri dish at 37°C. Initially, the liver and vascular cells fully occupy the left and right sides of the dish, respectively.
A) If the cells are allowed to mix randomly, what is the ΔS for this mixing process?
B) The only way for the initial arrangement of cells to persist is if its energy is lower than that of the mixed states. Assuming the mixed states all have the same energy, how much lower should the energy of the initial arrangement be to ensure that its probability is at least 99.9999%?