Constraint–Homogeneity Duality: A Universal Equation for Matter, Space, and Cognition

This paper introduces the universal relation Constraint×Homogeneity=Constant as a principle linking closed and open systems across disciplines. In closed systems—such as nuclei, electrons, the brain, or enclosed biological organs—physical quantities (volume, pressure, temperature, composition) are held constant, expressed as fn(x)=0. Confinement maximizes constraint but necessarily produces internal unevenness, giving rise to matter, subjectivity, and consciousness. In contrast, open systems lack strict constraints (fn(x)≠0); physical totals fluctuate, but distributions tend toward homogeneity. Radiation and diffusion thus characterize the external domain, which we recognize as space. This duality clarifies why matter persists as uneven localized phenomena, while space expands as an equalized continuum. Applications extend across physics (energy conservation vs. entropy growth), neuroscience (homeostasis and cognition), relativity (spacetime curvature as constrained deformation), chemistry (reaction selectivity via constraint convergence), and planetary science (internal concentration vs. external radiation). By framing matter as the internal subjective field and space as the external radiative field, the equation provides a compact explanatory law unifying thermodynamics, relativity, neuroscience, chemistry, and cosmology under a single principle.