Density fluctuations and entropy
Abstract
A new functional for the entropy that is asymptotically correct both in the high and low density limits is proposed. The new form is [ S=S^{(id)}+S^{(ln)}+S^{(r)}+S^{(c)} ] where the new term S^{(c)} depends on the p-bodies density fluctuations and has the form [ S^{(c)}= <N> {ln 2-1+\sum_{p=2}^\infty \frac{(\ln 2) ^p}{p!}\alpha_p-[ \exp (\alpha_2-1)-\alpha_2]} +\hat S ], where renormalizes the ring approximation S^{(r)}. This result is obtained by analyzing the functional dependence of the most general expression of the entropy: Two main results for S^{(c)} are proven: i) In the thermodynamic limit, only the functional dependence on the one body distribution function survives and ii) by summing to infinite order the leading contributions in the density a new numerical expression for the entropy is proposed with a new renormalized ring approximation included. The relationship of these results to the incompressible approximation to entropy is discussed.
Cite
@article{arxiv.cond-mat/0003230,
title = {Density fluctuations and entropy},
author = {J. A. Hernando and L. Blum},
journal= {arXiv preprint arXiv:cond-mat/0003230},
year = {2009}
}
Comments
7 pages, ref. [5] added and included in introduction and conclusions