Systems with Variable Particle Number

Abstract

In many situations, the number of particles of a given type is not exactly known or may vary during reactions taking place in the system. One example would be that of a photon gas. As previously mentioned, photons are continuously emitted and absorbed by matter and their number in general is not fixed. This is also the case for condensed-matter states, where interactions may modify the number of various excitation quanta, such as phonons. In high-energy physics, any number of particles may be created or annihilated during a collision process. Lastly, since the number of atoms or molecules constituting a macroscopic body can never be known exactly, it becomes useful to describe the body using the grand-canonical statistical ensemble, in which the number of particles is allowed to fluctuate.