In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution, probability measure, or frequency distribution of particles in a system over various possible states. The Boltzmann distribution appears in statistical mechanics when considering isolated (or nearly-isolated) systems of fixed composition that are in thermal equilibrium (equilibrium with respect to energy exchange).
The ratio of a Boltzmann distribution computed for two states is known as the Boltzmann factor and characteristically only depends on the states’ energy difference.
|Boltzmann distribution in state 2 (dimensionless)
|Boltzmann distribution in state 1 (dimensionless)
|Energy in state 1 (J)
|Energy in state 2 (J)
|The absolute temperature (K)