Speaker
Description
We revisit Schrödinger's riddle of the nature and maintenance of order in an increasingly disordered universe from the perspective of information geometry, the differential geometry of statistical manifolds of probability distributions. This framework provides a hierarchy of distinguishability diagnostics ranging from global relative-entropic measures to local Fisher–Rao metrics and higher-order Amari tensors. Using Gaussian maximum-entropy distributions and non-Gaussian Laplace distributions as paradigmatic examples, we show that states possessing identical negentropy exhibit nontrivial information-geometric distinguishability despite sharing the same disorder deficit. Distinguishability persists both on maximum-entropy manifolds, where negentropy vanishes identically, and on non-Gaussian manifolds characterized by identical nonzero negentropy. These examples show that negentropy quantifies disorder deficit, whereas information geometry quantifies structural differentiation among probability distributions. Information geometry therefore embeds entropy and negentropy within a broader hierarchy of distinguishability diagnostics, providing a higher-resolution framework for characterizing order, disorder, and distinguishable probabilistic structures.