The Cahn–Hilliard equation (after John W. Cahn and ) is an equation of mathematical physics which describes the process of phase separation, by which the two components of a binary fluid spontaneously separate and form domains pure in each component. If is the concentration of the fluid, with indicating domains, then the equation is written as Related to it is the Allen–Cahn equation, as well as the stochastic Cahn–Hilliard Equation and the stochastic Allen–Cahn equation.