Vector Information Metrics and the Foundations of Biological Coherence

Classical entropy measures prove inadequate in fully characterizing biological systems' informational structures. This paper introduces hyperdimensional coherence entropy—a vectorial metric capturing alignment and phase relationships in high-dimensional information spaces. We demonstrate that biological systems maintain low coherence entropy through a remarkably simple principle: they export high-dimensional noise while importing low-dimensional, coherent structures. This reframes life as a coherence-driven phenomenon that continuously manages entropy gradients in real time. By capturing the directional, multidimensional properties of biological information, our framework elucidates processes from metabolism to cognition to evolution as manifestations of coherence management. This coherence-based perspective resolves paradoxes between thermodynamic and information-theoretic approaches, potentially reshaping our understanding of life itself.