In thermodynamics, the Gibbs–Duhem equation describes the relationship between changes in chemical potential for components in a thermodynamic system:
where  is the number of moles of component  the infinitesimal increase in chemical potential for this component,  the entropy,  the absolute temperature,  volume and  the pressure.  is the number of different components in the system. This equation shows that in thermodynamics intensive properties are not independent but related, making it a mathematical statement of the state postulate. When pressure and temperature are variable, only  of  components have independent values for chemical potential and Gibbs' phase rule follows. The Gibbs−Duhem equation cannot be used for small thermodynamic systems due to the influence of surface effects and other microscopic phenomena.
The equation is named after Josiah Willard Gibbs and Pierre Duhem.