Maxwell-Boltzmann statistics

In statistical mechanics, Maxwell–Boltzmann statistics describes the average distribution of non-interacting material particles over various energy states in thermal equilibrium, and is applicable when the temperature is high enough or the particle density is low enough to render quantum effects negligible.

The expected number of particles with energy ${\displaystyle \varepsilon _{i}}$ for Maxwell–Boltzmann statistics is

where:

Equivalently, the number of particles is sometimes expressed as

where the index i now specifies a particular state rather than the set of all states with energy ${\displaystyle \varepsilon _{i}}$, and ${\displaystyle Z=\sum _{i}e^{-\varepsilon _{i}/kT}}$.

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