The problem is to show that for a fermionic gas the entropy is given by: [tex]\sigma=-\int d\epsilon D(\epsilon )[f(\epsilon )log(f(\epsilon )-(1-f(\epsilon )log(1-f(\epsilon )][/tex] where D(epsilon) is the derivative operator wrt epsilon, and f(epsilon) is fermi-dirac distribution function. Now what I think is that I only need to show that the entropy equals minus the integrand, but I'm not sure where did the minus come from. I mean the entropy is defined as logarithm of the number of possible states, the function that counts this number is: (f^f)*((1-f)^(1-f)) cause f counts the number of possible states there are below the chemical potential and 1-f above it, and we take a power of themselves because there sum equals the number of states of the system. but I don't where did the minus sign come from, can you help me on this? thanks in advance.