Boltzmann–Gibbs entropy in statistical mechanics

E45253

information measure statistical mechanical entropy thermodynamic entropy

Boltzmann–Gibbs entropy in statistical mechanics is the standard measure of disorder or uncertainty in a system, quantifying how many microscopic configurations correspond to a given macroscopic state and forming the basis of classical equilibrium statistical mechanics.

Observed surface forms (5)

Surface form	Occurrences
Boltzmann–Gibbs entropy	0
Boltzmann entropy	5
Boltzmann entropy formula	4
Gibbs entropy	3
Gibbs paradox	1

Statements (48)

Predicate	Object
instanceOf	information measure ⓘ statistical mechanical entropy ⓘ thermodynamic entropy ⓘ
additivityProperty	additive for statistically independent subsystems ⓘ
appearsOn	Boltzmann’s tombstone formula S = k_B ln W ⓘ
appliesTo	canonical ensemble ⓘ classical systems in equilibrium ⓘ grand canonical ensemble ⓘ microcanonical ensemble ⓘ
assumes	ergodic hypothesis ⓘ short-range interactions in typical applications ⓘ
basisOf	classical equilibrium statistical mechanics ⓘ
concavityProperty	concave functional of the probability distribution ⓘ
continuousVersionName	Boltzmann–Gibbs entropy in statistical mechanics self-linksurface differs ⓘ surface form: Gibbs entropy
contrastedWith	Rényi entropy ⓘ Tsallis entropy ⓘ
domain	continuous probability densities ⓘ discrete probability distributions ⓘ
field	information theory ⓘ statistical mechanics ⓘ thermodynamics ⓘ
historicalOrigin	late 19th century ⓘ
increasesWith	irreversible processes ⓘ
maximizationYields	Boltzmann distribution ⓘ
maximizedUnder	constraints on average energy ⓘ normalization of probabilities ⓘ
monotonicWith	number of accessible microstates ⓘ
namedAfter	Josiah Willard Gibbs ⓘ Ludwig Boltzmann ⓘ
quantifies	disorder ⓘ number of microscopic configurations compatible with a macroscopic state ⓘ uncertainty ⓘ
relatedTo	Boltzmann–Gibbs entropy in statistical mechanics self-linksurface differs ⓘ surface form: Boltzmann entropy Boltzmann–Gibbs entropy in statistical mechanics self-linksurface differs ⓘ surface form: Gibbs entropy H-theorem ⓘ Maxwell–Boltzmann statistics ⓘ surface form: Maxwell–Boltzmann distribution Shannon entropy ⓘ canonical partition function ⓘ second law of thermodynamics ⓘ
standardFormula	S = -k_B \sum_i p_i \ln p_i ⓘ S = k_B \ln W ⓘ
symbol	S ⓘ
unit	joule per kelvin ⓘ
usedFor	characterizing equilibrium states ⓘ defining free energy ⓘ defining temperature in statistical mechanics ⓘ deriving thermodynamic relations ⓘ
usesConstant	Boltzmann constant ⓘ

Referenced by (14)

Full triples — surface form annotated when it differs from this entity's canonical label.

Maxwell–Boltzmann statistics → basedOn → Boltzmann–Gibbs entropy in statistical mechanics ⓘ

this entity surface form: Boltzmann entropy formula

Shannon–Khinchin axioms → characterizes → Boltzmann–Gibbs entropy in statistical mechanics ⓘ

Boltzmann–Gibbs entropy in statistical mechanics → continuousVersionName → Boltzmann–Gibbs entropy in statistical mechanics self-linksurface differs ⓘ

subject surface form: Boltzmann–Gibbs entropy

this entity surface form: Gibbs entropy

Sackur–Tetrode equation → corrects → Boltzmann–Gibbs entropy in statistical mechanics ⓘ

this entity surface form: Gibbs paradox

Sackur–Tetrode equation → derivedFrom → Boltzmann–Gibbs entropy in statistical mechanics ⓘ

this entity surface form: Boltzmann entropy formula

Ludwig Boltzmann → knownFor → Boltzmann–Gibbs entropy in statistical mechanics ⓘ

this entity surface form: Boltzmann entropy formula

Boltzmann distribution → relatedConcept → Boltzmann–Gibbs entropy in statistical mechanics ⓘ

this entity surface form: Boltzmann entropy formula

H-theorem → relatedConcept → Boltzmann–Gibbs entropy in statistical mechanics ⓘ

this entity surface form: Gibbs entropy

Maxwell's demon thought experiment → relatedConcept → Boltzmann–Gibbs entropy in statistical mechanics ⓘ