Elementary Principles in Statistical Mechanics, Developed with Especial Reference to the Rational Foundation of Thermodynamics¶
Gibbs, J. W. (1902). Elementary Principles in Statistical Mechanics, Developed with Especial Reference to the Rational Foundation of Thermodynamics. Yale University Press.
Cited by¶
6 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Degrees of Freedom
- In statistical mechanics, the Gibbs ensemble
This sourceFounds equilibrium statistical mechanics on ensembles in phase space (microcanonical, canonical, grand-canonical); for N DOFs phase space has 2N dimensions, and macroscopic thermodynamics emerges as ensemble averages over phase-space configurations.
- In statistical mechanics, the Gibbs ensemble
- Ensemble
- In statistical mechanics, the ensemble concept became foundational through the work of J.W. Gibbs
This sourcethe founding systematic treatment of equilibrium ensembles (microcanonical, canonical, grand-canonical) as collections of microstates weighted by thermal probability, with ensemble averages recovering thermodynamic observables.
- Population: all microstates of a system in thermal contact with a heat bath at temperature T. Generating mechanism: microstate enumeration (or sampling) weighted by the Boltzmann factor exp(−E/kT), justified by Gibbs's principle
This sourceensembles of systems in thermal equilibrium with a heat bath at temperature T obey the Boltzmann distribution exp(−E/kT) over microstates, and the weighted ensemble average of an observable equals the thermodynamic observable.
- In statistical mechanics, the ensemble concept became foundational through the work of J.W. Gibbs
- Entropy (Thermodynamic Sense)
- Every thermodynamic-entropy articulation specifies (1) the macroscopic system and its thermodynamic variables (energy, volume, particle number, etc.); (2) the choice of statistical ensemble
This sourceFounds modern statistical mechanics; coins and develops the microcanonical, canonical, and grand-canonical ensembles and the ensemble (Gibbs) entropy S = −k Σ p ln p.
- Every thermodynamic-entropy articulation specifies (1) the macroscopic system and its thermodynamic variables (energy, volume, particle number, etc.); (2) the choice of statistical ensemble
- Phase Space
- Phase space appears in classical mechanics (Hamiltonian formulation; the fundamental setting for advanced mechanics and celestial mechanics); in statistical mechanics (ensemble theory — the distribution of system states in phase space, Liouville's theorem, ergodic theory);
This sourceProvides unified statistical-mechanical framework for equilibrium ensembles: microcanonical, canonical, and grand-canonical; shows how ensemble distributions generate equilibrium thermodynamics and how equilibrium states emerge as macroscopic consequences of ensemble averaging.
- Phase space appears in classical mechanics (Hamiltonian formulation; the fundamental setting for advanced mechanics and celestial mechanics); in statistical mechanics (ensemble theory — the distribution of system states in phase space, Liouville's theorem, ergodic theory);
- Thermodynamic Equilibrium
- in statistical mechanics (the Boltzmann-Gibbs distribution characterizes equilibrium ensembles)
This sourceProvides unified statistical-mechanical framework for equilibrium ensembles: microcanonical, canonical, and grand-canonical; shows how ensemble distributions generate equilibrium thermodynamics and how equilibrium states emerge as macroscopic consequences of ensemble averaging.
- in statistical mechanics (the Boltzmann-Gibbs distribution characterizes equilibrium ensembles)
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