1) Under certain isobaric isothermal conditions, the chemical potentials of the two phases must be equal.

2) The first partial derivatives of two-phase chemical potential to temperature t and pressure p are not equal, which means that there are latent heat of phase change and sudden change of volume during phase change (because latent heat of phase change is the first partial derivative of chemical potential to temperature t and sudden change of volume is the first partial derivative of chemical potential to pressure p).

What about continuous phase transition? In addition to the condition 1), the first-order partial derivative of chemical potential must be equal to temperature t and pressure p, and the second-order partial derivative (called second-order phase transition when it is not equal) is not needed. In the process of second-order phase transformation, various thermal parameters such as heat capacity, isothermal compression coefficient and expansion coefficient will suddenly change. Landau's continuous phase transition theory explains the abrupt change of these thermal parameters near the critical point. It attributed this mutation to the change of order and symmetry of matter.

Let's take uniaxial ferromagnet as an example to briefly explain Landau theory.

Landau regards spontaneous magnetization m as an order variable, which is a physical quantity describing the degree of order of matter. Obviously, when the temperature of m is lower than the critical temperature Tc, the order of m is higher, showing anisotropy, that is, ferromagnetism. When the temperature rises and reaches the critical temperature Tc, M=0, showing disorder, high symmetry and isotropy, that is, paramagnetism. With the increase of temperature, m changes from non-zero to zero, and from order to disorder. We can use m to express the mathematical expressions of m, h and x (magnetic susceptibility), and we will find that they have two different expressions near the critical temperature, which just shows that these parameters have a sudden change and a continuous phase change near the critical temperature. And through the calculation of m, h, x, we can get the critical index, so as to find some universal laws that do not depend on the characteristics of each substance.