thermodynamic potential
A thermodynamic potential is the right kind of 'energy' to watch depending on what you're holding steady — much as a hiker's relevant 'downhill' depends on which trail constraints they face. There isn't one universal energy that always points the way to equilibrium; instead there's a small family of them, each tailored to a particular set of conditions, and each one slides to its lowest value when the system reaches balance under those conditions.
The family has four main members. Internal energy U is the natural potential at constant entropy and volume; enthalpy H suits constant entropy and pressure; Helmholtz energy A is the one for constant temperature and volume; and Gibbs energy G governs constant temperature and pressure. Each is built from the others by swapping which variables you control, and each is minimized at equilibrium for its own set of held-fixed conditions.
Why it matters: picking the right potential turns hard questions into easy ones — you just ask which way it goes downhill. Chemists lean on Gibbs energy because labs run at constant temperature and pressure; engineers and physicists often want Helmholtz energy or enthalpy. The honest point is that these aren't four different energies in nature; they are four convenient viewpoints on the same underlying thermodynamics, chosen to match your experiment.
A reaction in an open flask (constant T and p) is judged by Gibbs energy; seal it in a rigid bomb (constant T and V) and the right judge becomes Helmholtz energy — same chemistry, different potential to minimize.
Match the potential to your held-fixed conditions, then follow it downhill.
The four potentials are linked by Legendre transforms — a mathematical recipe that swaps a controlled variable (say, entropy) for its conjugate (temperature). That's why moving from U to H to A to G feels like turning the same object to view it from a new angle.