Maxwell relations

The Maxwell relations in thermodynamics can be derived from the symmetry of second derivatives and the definitions of the thermodynamic potentials, or from Jacobian determinants. The most common Maxwell relations involve the potential functions (the total internal energy), (enthalpy), (Helmholtz free energy), and (Gibbs free energy), and the functions of state (pressure), (absolute temperature), (volume), and (entropy).

They are named for the physicist James Clerk Maxwell, who first presented them in his text Theory of Heat (1872). Maxwell's relations are useful in problem-solving quantities that are difficult to measure to those that are easier to work with. Numerous mnemonic devices exist for remembering them, notably, the thermodynamic square.

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