A comment on the relation between diffraction and entropy

TL;DR

This paper discusses the complex relationship between diffraction patterns and entropy in solids, highlighting that systems with identical diffraction can have different entropy levels, challenging previous assumptions.

Contribution

It provides a summary of current understanding through characteristic examples, emphasizing the nuanced relation between diffraction and entropy.

Findings

Homometric systems can share diffraction patterns but differ in entropy.

Pure point diffraction systems with zero entropy are uniquely ergodic.

The relation between diffraction and entropy is complex and not fully understood.

Abstract

Diffraction methods are used to detect atomic order in solids. While uniquely ergodic systems with pure point diffraction have zero entropy, the relation between diffraction and entropy is not as straightforward in general. In particular, there exist families of homometric systems, which are systems sharing the same diffraction, with varying entropy. We summarise the present state of understanding by several characteristic examples.