The partition function then takes the form of an integral.

This is what makes it different from the ordinary partition function.

Such is the case for the partition function in quantum field theory.

The same can be said for partition functions and any ensemble.

Thus a partition function can be defined for each mode.

Thus the partition function looks like the weight factor for the ensemble.

The denominator of the right side is the partition function.

Where is the closed form for the partition function.

This is a closed and exact expression for the partition function of the system.

This is the trivial term, which does not affect the partition function of the system.

In this case, the partition function equals the total number of valid states.

The partition function is calculated using a dynamic programming approach.

See partition function (statistical mechanics) for the case where the numbers in question are the energy levels of a physical system.

This is called the partition function of the canonical ensemble.

In either case, the partition function may be solved exactly using eigenanalysis.

In this case we must describe the partition function using an integral rather than a sum.

For simplicity, we will use the discrete form of the partition function in this article.

Expressions for the various molecular partition functions are shown in the following table.

Strictly speaking, though, this is the partition function for a statistical field theory.

The partition function in this limit is where is the ground state energy.

Thus they can be used as a kind of partition function for nonequilibrium steady states.

In analogy with statistical mechanics it is also called the partition function.

In that context, the normalizing constant is called the partition function.

Corner transfer matrices are related to the partition function in a simple way.

However, trying to compute the partition function from its definition is not practical.