The Boltzmann distribution is the discrete statistical distribution in which a state of energy 
has probability
 |
where
 |
and 
is the absolute temperature, 
is the Boltzmann constant that converts temperature
to energy, and the normalizing sum 
ensures that 
. Consequently, the ratio of the probabilities
of two states is 
.
At high temperature, states with different finite energies have more nearly equal probabilities. At low temperature, states of lower energy receive exponentially greater probability. If an energy value is shared by several states, the total probability of that energy level is multiplied by the number of states sharing it.
