This is a problem to do with statistical physics, and the exchange of energy when we have two microcanonical ensemble.
I don't understand why there should be a minus sign in the middle, if Energy* is the energy of system 1 , Energy total - E* is the energy of another system, Two system were put together and interact, I was told this equation can maximise entropy, but I can't really see why?
I thought S = (S1(E*))+S(E total - E*) is the total entropy. therefore it should be a positive sign when you differentiate..
Just to clarify, S(E*) and S(E total - E*) , they are just labels, not function of E* and E total - E*