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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

 M number of the state (dimensionless) n energy of state n (dimensionless) ϵn energy of state n (J) k Boltzmann constant T temperature of the system (K) e e ϵi energy of state i (J) pi probability of state i (dimensionless)