Maxwell relations

Maxwell's relations are a set of equations in thermodynamics that arise from the equality of mixed second derivatives of thermodynamic potentials. They provide a connection between different thermodynamic properties and facilitate calculations involving changes in state variables. Maxwell's relations are derived from the fundamental thermodynamic potentials: the internal energy \( U \), the Helmholtz free energy \( F \), the Gibbs free energy \( G \), and the enthalpy \( H \).