Identify the local chiral analogue of the electric dipole in finite systems

Identify the local quantity representing structural chirality in finite systems that serves as the chiral analogue of the electric dipole moment.

Background

The paper calls for a formal, quantitative theory of structural chirality analogous to the Modern Theory of Polarization. A key prerequisite is a local measure of chirality in finite systems, analogous to electric or magnetic dipole moments, which would underpin a bulk thermodynamic quantity termed chiralization in periodic crystals.

The authors note that previous attempts to quantify chirality (e.g., asymmetry products, chirality functions, similarity measures, continuous symmetry measures, and helicity-inspired definitions) have conceptual shortcomings and do not yield a rigorous, physically grounded order parameter. In contrast to polarization, where the local electric dipole is well defined even if bulk polarization in crystals required a modern theory, the chiral case currently lacks the foundational local analogue altogether.