# nLab Boltzmann distribution

Contents

## Surveys, textbooks and lecture notes

#### Measure and probability theory

measure theory

probability theory

# Contents

## 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).

## References

Named after Ludwig Boltzmann.