The stability of the grand microcanonical ensemble for bounded isothermal spheres

Details The stability of the grand microcanonical ensemble for bounded isothermal spheres The stability of the grand microcanonical ensemble for bounded isothermal spheres

Publishing date

Feb 1981

URL

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981apj...243..983l&link_type=abstract

Journals

Astrophysical Journal, Part 1, vol. 243, Feb. 1, 1981, p. 983-986.

Science

Other

Additional info 2

3

Additional info 3

Galactic Evolution, Globular Clusters, Isothermal Processes, Thermodynamic Equilibrium, Binary Stars, Canonical Forms, Gravitational Fields, Hydrodynamics, Spheres

Type

Scientific paper

Abstract

It is noted that the thermodynamic stability of self-gravitating, isothermal spheres is thought to have application to the late stages of globular cluster evolution. It is considered worthwhile to introduce a new ensemble, which treats the old constraints (conversion of energy and mass) in a new combination. Attention is given to the fact that the microcanonical ensemble, which constrains both the energy and the mass, is the most stable, while the grand canonical ensemble, which allows both the energy and mass to fluctuate, is the least stable. The canonical ensemble, which permits the energy to fluctuate (as fixed temperature) but constrains the mass, lies between the two. A new ensemble, referred to as the grand microcanonical, is introduced which constrains the energy but permits the mass to fluctuate. This ensemble becomes unstable for density contrasts exceeding 1.66 but becomes stable again for density contrasts between 11.6 and 92.6; thereafter it is unstable. Its behavior is thus analogous to that of the canonical ensemble, with fluctuation in the mass replacing fluctuation in the energy.

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