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.

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All labels observed (6)

Label	Occurrences
Boltzmann entropy	10
Boltzmann entropy formula	5
Gibbs entropy	4
Boltzmann–Gibbs entropy in statistical mechanics canonical	1
Boltzmann–Gibbs statistical mechanics	1
Gibbs paradox	1

How this entity was disambiguated

This entity first appeared as the object of triple T356724 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Boltzmann–Gibbs entropy in statistical mechanics
Context triple: [Shannon–Khinchin axioms, characterizes, Boltzmann–Gibbs entropy in statistical mechanics]

A. Tsallis entropy
Tsallis entropy is a generalized, nonadditive entropy measure in statistical mechanics and information theory that extends Shannon entropy to better describe complex, nonextensive systems.
B. Rényi entropy
Rényi entropy is a generalized measure of information and uncertainty that extends Shannon entropy by introducing a tunable order parameter to emphasize different aspects of a probability distribution.
C. Maxwell–Boltzmann statistics
Maxwell–Boltzmann statistics is a classical statistical framework in physics that describes the distribution of speeds or energies among distinguishable, non-quantum particles in thermal equilibrium.
D. Shannon–Khinchin axioms
The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
E. Bekenstein–Hawking entropy
Bekenstein–Hawking entropy is the thermodynamic entropy associated with a black hole, proportional to the area of its event horizon and fundamental in linking gravity, quantum theory, and thermodynamics.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Boltzmann–Gibbs entropy in statistical mechanics
Target entity description: 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.

A. Tsallis entropy
Tsallis entropy is a generalized, nonadditive entropy measure in statistical mechanics and information theory that extends Shannon entropy to better describe complex, nonextensive systems.
B. Rényi entropy
Rényi entropy is a generalized measure of information and uncertainty that extends Shannon entropy by introducing a tunable order parameter to emphasize different aspects of a probability distribution.
C. Maxwell–Boltzmann statistics
Maxwell–Boltzmann statistics is a classical statistical framework in physics that describes the distribution of speeds or energies among distinguishable, non-quantum particles in thermal equilibrium.
D. Shannon–Khinchin axioms
The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
E. Bekenstein–Hawking entropy
Bekenstein–Hawking entropy is the thermodynamic entropy associated with a black hole, proportional to the area of its event horizon and fundamental in linking gravity, quantum theory, and thermodynamics.
F. None of above. chosen

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	Gibbs entropy ⓘ linked to: Boltzmann–Gibbs entropy in statistical mechanics
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 entropy ⓘ linked to: Boltzmann–Gibbs entropy in statistical mechanics Gibbs entropy ⓘ linked to: Boltzmann–Gibbs entropy in statistical mechanics H-theorem ⓘ Maxwell–Boltzmann distribution ⓘ linked to: Maxwell–Boltzmann statistics 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 ⓘ

How these facts were elicited