The Helmholtz free energy is a useful quantity when studying thermodynamic transformations in which the temperature is held constant. Although the reduction in the number of variables is a useful simplification, the main advantage comes from the fact that the Helmholtz free energy is minimized at equilibrium with respect to any unconstrained internal variables for a closed system at constant temperature and volume. This follows directly from the principle of minimum energy which states that at constant entropy, the internal energy is minimized. This can be stated as: