Complexity in the stepwise ideal gas Carnot cycle

A stepwise Carnot cycle is performed by means of N small weights (here called dwʹs), which are first added and then removed from the piston of the vessel containing the gas. The size of the dwʹs affects the entropy production. The work performed by the gas can be found as increase of the potential energy of the dwʹs. We identify each single dw and thus evaluate its raising, i.e., its increase in potential energy. In such a way we find how the energy output of the cycle is distributed among the dwʹs. The distribution depends on the removing process we choose. Since these processes are N!, there are N! distributions of the raisings of the dwʹs; it is therefore worthwhile to investigate how to find ni=n( i) the number of the dwʹs whose energy increase is i.