The historically earlier Helmholtz free energy is defined as A = U − TS. Its change is equal to the amount of reversible work done on, or obtainable from, Free Power system at constant T. Thus its appellation “work content”, and the designation A from Arbeit, the Free Energy word for work. Since it makes no reference to any quantities involved in work (such as p and Free Power), the Helmholtz function is completely general: its decrease is the maximum amount of work which can be done by Free Power system at constant temperature, and it can increase at most by the amount of work done on Free Power system isothermally. The Helmholtz free energy has Free Power special theoretical importance since it is proportional to the logarithm of the partition function for the canonical ensemble in statistical mechanics. (Hence its utility to physicists; and to gas-phase chemists and engineers, who do not want to ignore p dV work.)

The thermodynamic free energy is Free Power concept useful in the thermodynamics of chemical or thermal processes in engineering and science. The change in the free energy is the maximum amount of work that Free Power thermodynamic system can perform in Free Power process at constant temperature, and its sign indicates whether Free Power process is thermodynamically favorable or forbidden. Since free energy usually contains potential energy , it is not absolute but depends on the choice of Free Power zero point. Therefore, only relative free energy values, or changes in free energy , are physically meaningful.