I was looking at a derivation of entropy expressed as an absolute probability: S = -k. SUM P.lnP (What is the name of this by the way?) In the derivation, it makes the following statements which I really just dont get! U = SUM E.P so therefore dU = SUM E.dP - SUM P.dE Where does the minus sign come from? Should it not be a plus?? Then, it goes from dS = -k. SUM lnP.dP to dS = -k.d(SUM P.lnP) How is that true?? First it was just P that was a differential element, now its the whole expression in the bracket??