# Boltzmann factor 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 ratio of a Boltzmann distribution computed for two states is known as the Boltzmann factor and characteristically only depends on the states’ energy difference. it is expressed as shown

Related formulas## Variables

F_{state1} | Boltzmann distribution of state 1 (dimensionless) |

F_{state2} | Boltzmann distribution of state 2 (dimensionless) |

E_{1} | state 1 energy (J) |

E_{2} | state 2 energy (J) |

k | Boltzmann constant |

T | temperature of the system (K) |