Boltzmann distribution
E46139
The Boltzmann distribution is a fundamental probability distribution in statistical mechanics that describes how particles or states are populated over different energy levels at thermal equilibrium.
Observed surface forms (2)
| Surface form | Occurrences |
|---|---|
| Boltzmann factor | 1 |
| Gibbs distribution | 1 |
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
concept in statistical mechanics
ⓘ
probability distribution ⓘ |
| appliesTo | systems in thermal equilibrium ⓘ |
| approximationOf |
Bose–Einstein distribution at high temperature and low density
ⓘ
Fermi–Dirac distribution at high temperature and low density ⓘ |
| assumes | classical distinguishable particles in many applications ⓘ |
| contrastsWith |
Bose–Einstein statistics
ⓘ
surface form:
Bose–Einstein distribution
Fermi–Dirac statistics ⓘ
surface form:
Fermi–Dirac distribution
|
| dependsOn |
Boltzmann constant
ⓘ
energy of the state ⓘ temperature ⓘ |
| describes | probability of a system occupying a state with given energy at thermal equilibrium ⓘ |
| field |
physics
ⓘ
statistical mechanics ⓘ thermodynamics ⓘ |
| hasComponent | Boltzmann factor exp(-E/(k_B T)) ⓘ |
| hasMathematicalForm | P(E) ∝ exp(-E/(k_B T)) ⓘ |
| implies | higher energy states are less populated than lower energy states ⓘ |
| namedAfter | Ludwig Boltzmann ⓘ |
| normalizationCondition | sum over all states of P(E_i) = 1 ⓘ |
| relatedConcept |
Boltzmann–Gibbs entropy in statistical mechanics
ⓘ
surface form:
Boltzmann entropy formula
grand canonical ensemble ⓘ microcanonical ensemble ⓘ |
| relatedTo |
Boltzmann distribution
self-linksurface differs
ⓘ
surface form:
Boltzmann factor
Boltzmann distribution self-linksurface differs ⓘ
surface form:
Gibbs distribution
Maxwell–Boltzmann statistics ⓘ
surface form:
Maxwell–Boltzmann distribution
canonical ensemble ⓘ partition function ⓘ |
| temperatureEffect | higher temperature increases population of higher energy states ⓘ |
| usedFor |
calculating average energy
ⓘ
calculating entropy in canonical ensemble ⓘ calculating heat capacity ⓘ deriving macroscopic thermodynamic quantities ⓘ population of electronic energy levels ⓘ population of energy levels in gases ⓘ population of molecular rotational states ⓘ population of molecular vibrational states ⓘ |
| usedIn |
astrophysics
ⓘ
chemical equilibrium calculations ⓘ laser physics ⓘ molecular simulations ⓘ plasma physics ⓘ reaction rate theory ⓘ spectroscopy ⓘ |
| usesSymbol |
E for energy
ⓘ
T for absolute temperature ⓘ k_B for Boltzmann constant ⓘ |
| validWhen |
system is ergodic
ⓘ
system is in contact with a heat bath at fixed temperature ⓘ |
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Boltzmann–Gibbs entropy
this entity surface form:
Gibbs distribution
this entity surface form:
Boltzmann factor