the Helmholtz free energy, an environment at constant temperature T will contribute an amount TS to the system, reducing the overall investment necessary for creating the system. This net energy contribution for a system created in environment temperature T from a negligible initial volume is the Gibbs free energy.
The Helmholtz free energy is of interest mainly to chemical engineers (whose industrial-scale processes are often confined to tanks and reactors of fixed volume) and some geochemists whose interest is centered on the chemistry that occurs deep within the earth's surface.
The free energy enables us to do this for changes that occur at a constant temperature and pressure (the Gibbs free energy) or constant temperature and volume (the Helmholtz free energy.)
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