Generalized canonical ensembles and ensemble equivalence
arXiv:cond-mat/0505218 · doi:10.1103/PhysRevE.73.026105
Abstract
This paper is a companion article to our previous paper (J. Stat. Phys. 119, 1283 (2005), cond-mat/0408681), which introduced a generalized canonical ensemble obtained by multiplying the usual Boltzmann weight factor of the canonical ensemble with an exponential factor involving a continuous function of the Hamiltonian . 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 , the generalized canonical ensemble reproduces, in the thermodynamic limit, all the microcanonical equilibrium properties of the many-body system represented by even if this system has a nonconcave microcanonical entropy function. This is something that in general the standard () canonical ensemble cannot achieve. Thus a virtue of the generalized canonical ensemble is that it can be made equivalent to the microcanonical ensemble in cases where the canonical ensemble cannot. The case of quadratic -functions is discussed in detail; it leads to the so-called Gaussian ensemble.
8 pages, 4 figures (best viewed in ps), revtex4. Changes in v2: Title changed, references updated, new paragraph added, minor differences with published version
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