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Boltzmann distribution in mechanics

Description

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. In statistical mechanics, the Boltzmann distribution is a probability distribution that gives the probability that a system will be in a certain state as a function of that state’s energy and the temperature of the system. 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 shown.

Related formulas

Variables

Mnumber of the state (dimensionless)
nenergy of state n (dimensionless)
ϵnenergy of state n (J)
kBoltzmann constant
Ttemperature of the system (K)
ee
ϵienergy of state i (J)
piprobability of state i (dimensionless)