[1] The particle number is a fundamental thermodynamic property which is conjugate to the chemical potential.
A constituent particle is one that cannot be broken into smaller pieces at the scale of energy k·T involved in the process (where k is the Boltzmann constant and T is the temperature).
If the material is homogeneous and has a known amount of substance n expressed in moles, the particle number N can be found by the relation :
This parameter is often denoted by the lower-case letter n. In quantum mechanical processes, the total number of particles may not be preserved.
In the current EU emission norms for cars, vans, and trucks and in the upcoming EU emission norm for non-road mobile machinery, particle number measurements and limits are defined, commonly referred to as PN, with units [#/km] or [#/kWh].