1. The problem statement, all variables and given/known data Show that the free energy, F=SUM(E_i*p_i)+T*SUM(p_i*ln(p_i)) is minimal when p_i=e^(-E_i/T)/SUM(e^(-E_i/T)) Where E is energy, T is temperature 2. Relevant equations Nothing really 3. The attempt at a solution So if I just try and find the derivative of the force I arrive at something along the lines of p_i=e^((-E_i/T)-1). I'm assuming I'm supposed to use some constraints to show that the entropy is fixed but I'm not sure how to go about doing that.