Ensembles in thermostatistics

Thermostatistical ensembles are collectives whose average behaviour reflects the actual behaviour of a physical system.

History

The concept of thermostatistical ensembles was introduced by Josiah Willard Gibbs (Ref. 1). Albert Einstein also also, independently, introduced ensembles (Refs. 2 and 3).

Representative ensembles

• Canonical ensemble ($NVT$)
• Gibbs ensemble
• Grand canonical ensemble ($\mu VT$)
• Isothermal-isobaric ensemble ($NpT$)
• Microcanonical ensemble ($NVE$)

See also

• Gibbs ensemble Monte Carlo
• Monte Carlo in the grand-canonical ensemble
• Monte Carlo in the microcanonical ensemble

References

1. Josiah Willard Gibbs "Elementary principles in statistical mechanics developed with especial reference to the rational foundation of thermodynamics" (1902) (scanned page images in PDF format)
2. A. Einstein "Kinetische Theorie des Wärmegleichgewichtes und des zweiten Hauptsatzes der Thermodynamik", Annalen der Physik 9 pp. 417-433 (1902)
3. A. Einstein "Eine Theorie der Grundlagen der Thermodynamik", Annalen der Physik 11 pp. 170-187 (1903)
4. Richard C. Tolman "On the Establishment of Grand Canonical Distributions", Physical Review 57 pp. 1160-1168 (1940)