I was reading the Wikipedia page about Helmholtz free energy and there is a sentence I don't get:
We see that the total amount of work that can be extracted in an isothermal process is limited by the free-energy decrease, and that increasing the free energy in a reversible process requires work to be done on the system. If no work is extracted from the system, then $$\Delta F \leq 0$$
and thus for a system kept at constant temperature and volume and not capable of performing electrical or other non-''PV'' work, the total free energy during a spontaneous change can only decrease.
This result seems to contradict the equation dF = −S dT − P dV, as keeping T and V constant seems to imply dF = 0, and hence F = constant. In reality there is no contradiction: In a simple one-component system, to which the validity of the equation dF = −S dT − P dV 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.
I really don't understand why there is no contradiction. For a one-component system in contact with heat bath, why there is no process that occurs at constant T and V? What is "unique P(T, V) relation"?