This result seems to contradict the equation d"F" = −"S" d"T" − "P" d"V", as keeping "T" and "V" constant seems to imply d"F" = 0, and hence "F" = constant. In reality there is no contradiction: In a simple one-component system, to which the validity of the equation d"F" = −"S" d"T" − "P" d"V" is restricted, no process can occur at constant "T" and "V", since there is a unique "P"("T", "V") relation, and thus "T", "V", and "P" are all fixed. To allow for spontaneous processes at constant "T" and "V", one needs to enlarge the thermodynamical state space of the system. In case of a chemical reaction, one must allow for changes in the numbers "N""j" of particles of each type "j". The differential of the free energy then generalizes to