Density fluctuations and entropy

Journal Article · Wed Nov 01 04:00:00 EST 2000 · Physical Review E

DOI:https://doi.org/10.1103/PhysRevE.62.6577· OSTI ID:40205404

Hernando, J A; Blum, L

A functional for the entropy that is asymptotically correct both in the high- and low-density limits is proposed. The new form is S=S{sup (id)}+S{sup (ln)}+S{sup (r)}+S{sup (c)}, where the term S{sup (c)} depends on the p-body density fluctuations {alpha}{sub p} and has the form S{sup (c)}/k=<N>{l_brace}ln2-1+{Sigma}{sub p=2}{sup {infinity}}(ln2){sup p}/p!{alpha}{sub p}-[exp({alpha}{sub 2}-1)-{alpha}{sub 2}]{r_brace}+{cflx S}. {cflx S} renormalizes the ring approximation S{sup (r)}. This result is obtained by analyzing the functional dependence of the most general expression of the entropy. Two main results for S{sup (c)} are proved: (i) In the thermodynamic limit it is only a functional of the one-body distribution function and (ii) by summing to infinite order the leading contributions in the density a numerical expression for the entropy [Eq. (33)] with a renormalized ring approximation is obtained. The relation of these results to the incompressible approximation for the entropy is discussed and preliminary numerical results on hard spheres are presented.

• Sponsoring Organization: (US)
• OSTI ID: 40205404
• Journal Information: Physical Review E, Journal Name: Physical Review E Journal Issue: 5 Vol. 62; ISSN 1063-651X
• Publisher: The American Physical Society
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DISTRIBUTION FUNCTIONS
ENTROPY
FLUCTUATIONS
FUNCTIONALS
THERMODYNAMICS