# 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) |

ϵ_{n} | energy of state n (J) |

k | Boltzmann constant |

T | temperature of the system (K) |

e | e |

ϵ_{i} | energy of state i (J) |

p_{i} | probability of state i (dimensionless) |