Entropy Multiparticle Correlation Expansion for a Crystal

TL;DR

This paper extends the entropy correlation expansion concept from fluids to crystalline solids, providing a theoretical framework and numerical validation for the extensivity of entropy components in crystals.

Contribution

It introduces a correlation expansion for the entropy of crystals, analogous to that of fluids, and analyzes how entropy components scale with crystal size.

Findings

One- and two-body entropies scale extensively with crystal size.

Numerical data supports the correlation expansion for crystalline entropy.

Theoretical arguments confirm the extensivity of entropy contributions.

Abstract

As first shown by H. S. Green in 1952, the entropy of a classical fluid of identical particles can be written as a sum of many-particle contributions, each of them being a distinctive functional of all spatial distribution functions up to a given order. By revisiting the combinatorial derivation of the entropy formula, we argue that a similar correlation expansion holds for the entropy of a crystalline system. We discuss how one- and two-body entropies scale with the size of the crystal, and provide fresh numerical data to check the expectation, grounded on theoretical arguments, that both entropies are extensive quantities.