The Dimensional Cost of Erasure: Dissipative Systems, Landauer Limits, and the Hidden Structure of Noise

This paper proposes a fundamental reconceptualization of information dynamics by linking dissipation, dimensionality, and information preservation. Building on Landauer’s principle and Prigogine’s dissipative structures, I argue that information era- sure constitutes not merely an energy cost but a dimensional collapse—a quantifiable reduction in a system’s potential manifold of states. Systems that resist deterministic erasure preserve critical correlations that enable dimensional expansion and emergent complexity. I demonstrate how the seemingly random “noise” in biological and physical systems often contains hidden manifolds of coherence that support adaptation and intelligence, quantifiable through measures of effective dimensionality and multivariate mutual information. This stands in contrast to deterministic computational systems which, in their pursuit of clarity, systematically eliminate dimensionality through era- sure operations. This framework offers new insights into the nature of complexity, adaptability, and the thermodynamic foundations of intelligence, with testable predictions across physical, biological, and computational domains.