Entropy, in both thermodynamic and informational contexts, quantifies uncertainty and the amount of hidden or unknowable data within a system. In information theory, introduced by Claude Shannon, entropy reflects the average unpredictability of a message or state—higher entropy means greater uncertainty, and thus more information is needed to reduce it. In crystallography, entropy manifests in the disorder of atomic arrangements: even in a perfectly symmetric crystal, thermal vibrations introduce micro-entropic fluctuations that encode subtle structural information. This duality—ordered symmetry masked by probabilistic disorder—reveals how hidden information arises from measurable yet incomplete knowledge.Explore the Biggest Vault: where entropy meets security