nLab Boltzmann distribution

Idea

In thermodynamics, the Boltzmann distribution is the probability distribution on the space of configurations of a physical system which maximizes the entropy subject to the constraint that the expectation value of the energy is fixed.

It is characterized by a probability density proportional to the exponential of the energy weighted my minus the inverse temperature:

$$d p \;\propto\; e^{ - \frac{E}{k T} } \, d E \,,$$

where $k$ is Boltzmann's constant (a physical unit).

Related concepts

• Boltzmann constant

• inverse temperature

References

Named after Ludwig Boltzmann.

See also:

• Wikipedia, Boltzmann distribution