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The entropy functional for a discrete classical ensemble, with integral and quantum trace analogues subject to their measure and coarse-graining conventions.
wp-physics-gibbs-entropywp-physics-entropytong-statistical-physicsEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Gibbs entropy is a functional of the ensemble probabilities or density operator, with the reference measure and quantum trace specified.
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
wp-physics-gibbs-entropywp-physics-statistical-ensembletong-statistical-physicsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Under equilibrium, extensivity, and thermodynamic-limit assumptions, the appropriate ensemble entropy reproduces macroscopic thermodynamic entropy up to conventional additive constants. The relation can fail or require care for nonequivalent ensembles and long-range systems.
The target is recovered from the source either in a stated mathematical or asymptotic limit, or through a quantitatively controlled approximation with identified small parameters or omitted terms. The edge label and detail must state which case applies and its regime of validity.
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