Boltzmann factor
From Wikipedia, the free encyclopedia
In physics, the Boltzmann factor is a weighting factor that determines the relative probability of a state in a system in thermodynamic equilibrium at a temperature (T).
Where kB is Boltzmann's constant, and E is energy.
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 divides it by the sum Z of the Boltzmann factors of all possible states of a system, which is called the partition function. This gives the Boltzmann distribution.
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.
[edit] See also
- Boltzmann relation (plasma physics)
[edit] References
- Charles Kittel and Herbert Kroemer, Thermal Physics, 2nd ed. (Freeman & Co.: New York, 1980).
