Although the formula of chemical potential in a multi-component condensed matter is derived from the configuration entropy, this method is based on not thermodynamics but statistical mechanics. In this page, it is derived purely based on thermodynamics, whose starting point is the Gibbs energy of an ideal gas.

Here, the chemical potential in multi-component condensed matters at standard and high pressures in the following order.

1. Chemical potential of single-component condensed matter at standard pressure

2. Chemical potential of multi-component condensed matter at standard pressure

3. Chemical potential of multi-component condensed matter at high pressure