In physics, the Boltzmann factor is a weighting factor determining the relative probability of a system in thermodynamic equilibrium at a temperature T being in a state with energy E: Wikibooks Wikiversity has more about this subject: School of Physics sci. ... In thermodynamics, a thermodynamic system is in thermodynamic equilibrium if its energy distribution equals a Maxwell-Boltzmann-distribution. ... Temperature is the physical property of a system which underlies the common notions of hot and cold; the material with the higher temperature is said to be hotter. ...

(k_B is Boltzmann's constant.) This is not a probability function by itself, because it is not normalized. However, the ratio of the probabilities of two states is given by the ratio of their Boltzmann factors. To normalize the Boltzmann factor into a probability, one simply divides it by the sum Z of the Boltzmann factors of all possible states of a system, which sum is called the partition function. The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ... The word probability derives from the Latin probare (to prove, or to test). ... In statistical mechanics, the partition function Z is an important quantity that encodes the statistical properties of a system in thermodynamic equilibrium. ...

From the Boltzmann factor, one can then derive the Maxwell-Boltzmann statistics, Bose-Einstein statistics, and Fermi-Dirac statistics that govern classical particles as well as quantum mechanical bosons, and fermions, respectively. The Maxwell-Boltzmann distribution is a probability distribution with applications in physics and chemistry. ... For other topics related to Einstein see Einstein (disambig) In statistical mechanics, Bose-Einstein statistics determines the statistical distribution of identical indistinguishable bosons over the energy states in thermal equilibrium. ... In statistical mechanics, Fermi-Dirac statistics determines the statistical distribution of fermions over the energy states for a system in thermal equilibrium. ... A particle is In particle physics, a basic unit of matter or energy. ... Fig. ... Boson (game) Bosons, named after Satyendra Nath Bose, are particles which form totally-symmetric composite quantum states. ... Fermions, named after Enrico Fermi, are particles which form totally-antisymmetric composite quantum states. ...

See also

• Boltzmann relation

In a plasma, the Boltzmann relation connects the electron density ne to the plasma potential φpl as follows: ne = n0 exp(eφpl/kBTe) The reference for the potential potential is taken to be a position where the electron density is n0. ...

References

• Charles Kittel and Herbert Kroemer, Thermal Physics, 2nd ed. (Freeman & Co.: New York, 1980).