The Role of Information Entropy in Symmetry of Euclidean Polygons
Year: 2026
Type: article
Abstract: In this paper we investigate the relationship between Shannon information entropy and symmetry in closed Euclidean polygons within the framework of the second law of information dynamics. Using Lagrange multiplier formalism, we derive the condition for minimum entropy in a system of fixed size, showing that it occurs when all elements have equal multiplicity. Applying this result to two-dimensional polygons, we demonstrate that zero-symmetry configurations maximize entropy, while maximally symmetric shapes correspond to minimum entropy states. We show that although entropy increases with geometric descriptor complexity for asymmetric shapes, it remains invariant for maximally symmetric configurations. These results provide a quantitative basis for the association between symmetry and low information entropy, within the broader framework of information dynamics and entropy minimization principles.
Source: Entropy
DOI: 10.3390/e28050564
Author: Melvin M. Vopson
Institutions: Information Physics Institute, University of Portsmouth
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7161702693
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