When temperature and volume are taken to be constant chemical potential relates to the Helmholtz free energy, A.

For these studies, Helmholtz free energy is used.

As an example of another thermodynamic potential, the Helmholtz free energy is written:

For example, the Helmholtz free energy may be written:

This can be contrasted to the canonical partition function above, which is related instead to the Helmholtz free energy.

It follows from this that the differential of the Helmholtz free energy is:

For example, in explosives research, Helmholtz free energy is often used since explosive reactions by their nature induce pressure changes.

We may integrate the expression for to obtain the Helmholtz energy:

This page details the Helmholtz energy from the point of view of thermal and statistical physics.

At constant volume, one must consider the Helmholtz free energy for the reaction: A.