Related Experiment Video
Updated: May 28, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
Published on: July 19, 2016
The Role of Information Entropy in Symmetry of Euclidean Polygons
1School of Mathematics and Physics, University of Portsmouth, Portsmouth PO1 3QL, UK.
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.
Related Concept Videos
Gauss's Law: Planar Symmetry
Entropy
Entropy
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
Entropy and the Second Law of Thermodynamics
The relation between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
Entropy and the Second Law of Thermodynamics
Gauss's Law: Spherical Symmetry
