Particle statistics

A key prerequisite concept is that of a statistical ensemble (an idealization comprising the state space of possible states of a system, each labeled with a probability) that emphasizes properties of a large system as a whole at the expense of knowledge about parameters of separate particles.

In the language of quantum mechanics this means that the wave function of the system is invariant up to a phase with respect to the interchange of the constituent particles.

In the case of a system consisting of particles of different kinds (for example, electrons and protons), the wave function of the system is invariant up to a phase separately for both assemblies of particles.

Progressively more "complex" particles obtain progressively more internal freedoms (such as various quantum numbers in an atom), and, when the number of internal states that "identical" particles in an ensemble can occupy dwarfs their count (the particle number), then effects of quantum statistics become negligible.

That's why quantum statistics is useful when one considers, say, helium liquid or ammonia gas (its molecules have a large, but conceivable number of internal states), but is useless applied to systems constructed of macromolecules.