This kind of system is called a canonical ensemble.

This is the characteristic state function for the grand canonical ensemble.

This article derives some basic elements of the canonical ensemble.

This corresponds to studying the system in the canonical ensemble.

Let's rework everything using a grand canonical ensemble this time.

Alternatively, one can make use of the canonical ensemble.

It is derived in the same way as the partition function for the canonical ensemble.

Canonical ensemble: describes a system in thermal equilibrium with its environment.

To clarify, this is not a grand canonical ensemble.

A system kept at constant volume, temperature, and particle number is described by the canonical ensemble.

In other words, each single-particle level is a separate, tiny grand canonical ensemble.

Gibbs measure is widely used in statistical mechanics, often under the name canonical ensemble.

In a canonical ensemble, a system is in thermal contact with a reservoir.

(For a detailed derivation of this result, see canonical ensemble).

By abstracting away the reservoir, we will arrive at the grand canonical ensemble.

In the canonical ensemble, the partition function of the system can be written as:

In grand canonical ensemble V, T and chemical potential are fixed.

In a canonical ensemble, there is no exchange of particles, so the term is zero.

It underpins the concept of the canonical ensemble, providing the underlying distribution.

The grand canonical ensemble may also be used to describe classical systems, or even interacting quantum gases.

The particle number and energy in the system have natural fluctuations in the grand canonical ensemble.

Partition function (mathematics), a generalized review of canonical ensemble concepts.

A generalization of this is the grand canonical ensemble, in which the systems may share particles as well as energy.

The usefulness of the grand canonical ensemble is illustrated in the examples below:

Thus each orbital is a grand canonical ensemble unto itself, one simple that its statistics can be immediately derived here.