= Thermodynamic free energy
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= Free energy
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A <free energy> is a <thermodynamic potential> that compares possible states under specified environmental constraints. For a <closed system> of fixed composition, treated as a <simple compressible system> with only <pressure>-<volume (thermodynamics)> <work>, stable <thermodynamic equilibrium> minimizes <Helmholtz free energy> at fixed <temperature> and <volume (thermodynamics)>, or <Gibbs free energy> at fixed <temperature> and <pressure>. The choice follows the experiment: a rigid sealed vessel and a sealed cylinder with a freely moving loaded piston impose different constraints. Both may exchange <heat> with a <thermal reservoir>. See https://ocw.mit.edu/courses/3-00-thermodynamics-of-materials-fall-2002/14c95abd6fac023d84bd33c5d74d787d_lecture_02_oneside.PDF[W. C. Carter, MIT thermodynamics notes, sections 2-1.14 and 2-1.19].
\Image[/thermodynamic-potential-constraints.png]
{title=Choose <Helmholtz free energy> for fixed <temperature> and <volume (thermodynamics)>, or <Gibbs free energy> for fixed <temperature> and <pressure>}
{description=Original schematic of two closed vessels in contact with a <thermal reservoir>. Composition is fixed, and only <pressure>-<volume (thermodynamics)> <work> is allowed. The right piston permits the <volume (thermodynamics)> to change.}
The useful insight is that <internal energy> alone cannot rank these alternatives: exchanging <heat> also changes the surroundings' <entropy>. Subtracting $TS$ packages that accounting into a property of the chosen system. Adding $pV$ additionally accounts for displacing the surroundings at fixed <pressure>. A <free energy> is a <state function>; supplied <heat> describes a transfer during a process. Under the stated constraints, supplied <heat> is $Q=\Delta U$ at fixed <volume (thermodynamics)> or $Q=\Delta H$ at fixed <pressure>, whereas neither $\Delta F$ nor $\Delta G$ generally equals $Q$.
A lower <free energy> identifies a thermodynamic preference, without specifying a timescale. A barrier can trap a system in a <local minimum>, producing <metastability> although a lower <global minimum> exists. The <enzyme> example illustrates the corresponding distinction for <chemical reactions>: changing the route can change the <reaction rate> while preserving the endpoint <Gibbs free energy> difference and <chemical equilibrium>.
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