The population of the lower excited state is then given by the Boltzmann distribution.

This effect can be illustrated with a Boltzmann distribution and energy profile diagram.

The Boltzmann distribution is, however, much more general.

The algorithm samples secondary structures according to the Boltzmann distribution.

Base pair probabilities are estimated using an estimate similar to Boltzmann distribution.

The diffusion is according to the Boltzmann distribution exponentially related to the temperature.

It is a special case of a normalizing constant in probability theory, for the Boltzmann distribution.

In the first approximation, it is thus simply given by the Boltzmann distribution law:

The populations of these levels are determined by the Boltzmann distribution at a steady temperature and will essentially be equal.

In more general mathematical settings, the Boltzmann distribution is also known as the Gibbs measure.

(See that article for a derivation of the Boltzmann distribution.)

These fluctuations happen on time scales which are much larger than the microscopic relaxation times to the Boltzmann distribution.

This screening causes a Boltzmann distribution of electrons to form around the electric potentials.

This relation reflects the Boltzmann distribution of the ions with the energy qψ.

The exponential in the Boltzmann distribution should not be equal to 1 to obtain unequal populations.

In the above discussion, the Boltzmann distribution function was obtained via directly analysing the multiplicities of a system.

They are named after the Boltzmann distribution in statistical mechanics, which is used in their sampling function.

The configuration probability is given by the Boltzmann distribution with inverse temperature :

The Boltzmann distribution applied to a specific pair of amino acids, is given by:

The population of different conformers follows a Boltzmann distribution:

The resulting states are then sampled according to the Boltzmann distribution of the super state at temperature T.

We describe the ambient plasma by a Boltzmann distribution over the double layer:

Thus they obey Boltzmann statistics and form a Boltzmann distribution.

The probability of a phonon to have energy E is given by the Boltzmann distribution .

In the microwave region, the Boltzmann distribution of molecules among energy states is such that, at room temperature all states are populated almost equally.