Grand potential

The grand potential, even Landau potential for Lew Landau, is a used in statistical mechanics thermodynamic potential, which is mainly used for irreversible processes in open systems.

The grand potential is defined by:

In which

Respectively. alternatively, the grand potential are defined by the grand canonical partition function:

In place of sometimes, or used.

Because of the thermodynamic Euler equation, the grand potential is identical with

With

An infinitesimal change of the grand canonical potential is given by

At constant temperature ( ) and constant chemical potential ( = 0) strives for the grand potential of a thermodynamic system, which is left without a job turnover itself ( ), a minimum to ().

How to read directly from the above equation, the thermodynamic quantities, entropy, pressure and particle number as follows can be obtained: