Generalized canonical ensembles and ensemble equivalence
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003 (United States)
- School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS (United Kingdom)
This paper is a companion piece to our previous work [J. Stat. Phys. 119, 1283 (2005)], which introduced a generalized canonical ensemble obtained by multiplying the usual Boltzmann weight factor e{sup -{beta}}{sup H} of the canonical ensemble with an exponential factor involving a continuous function g of the Hamiltonian H. We provide here a simplified introduction to our previous work, focusing now on a number of physical rather than mathematical aspects of the generalized canonical ensemble. The main result discussed is that, for suitable choices of g, the generalized canonical ensemble reproduces, in the thermodynamic limit, all the microcanonical equilibrium properties of the many-body system represented by H even if this system has a nonconcave microcanonical entropy function. This is something that in general the standard (g=0) canonical ensemble cannot achieve. Thus a virtue of the generalized canonical ensemble is that it can often be made equivalent to the microcanonical ensemble in cases in which the canonical ensemble cannot. The case of quadratic g functions is discussed in detail; it leads to the so-called Gaussian ensemble.
- OSTI ID:
- 20778700
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 73, Issue 2; Other Information: DOI: 10.1103/PhysRevE.73.026105; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
Similar Records
On the Local Equivalence Between the Canonical and the Microcanonical Ensembles for Quantum Spin Systems
Particle number fluctuations in the microcanonical ensemble