The Boltzmann distribution is a probability distribution that gives the probability of a certain state as a function of that state's energy and temperature of the system to which the distribution is applied. It is given as p i = 1 Q exp ⁡ ⁡ ( − − ε ε i k T ) = exp ⁡ ⁡ ( − − ε ε i k T ) ∑ ∑ j = 1 M exp ⁡ ⁡ ( − − ε ε j k T )