The particle number, N, is the number of so called 'elementary particles' (or elementary constituents) in a thermodynamical system. The particle number is a fundamental parameter in thermodynamics and it is conjugate to the chemical potential.
By calling a constituent element, we state that it 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). Our definition of elementary particle is thus temperature dependent.
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