GeometricThermodynamicsI:TheBlackHoleConstantandtheUniversal Energy-InformationRelation

This preprint introduces the foundational framework of Geometric Thermodynamics, proposing a universal energy–information relation rooted in black hole physics. We identify a fundamental constant—dubbed the black hole constant \kappa_B = \frac{4\pi G}{\hbar c^5} = \frac{1}{E_P^2},κB=ℏc54πG=EP21, where E_PEP is the Planck energy—and postulate that the structural information content of a physical system scales as N_{\text{struct}} = \kappa_B E_{\text{irr}}^2Nstruct=κBEirr2 , with E_{\text{irr}}Eirr representing the irreducible (non-extractable) energy. This relation unifies the thermodynamic description of black holes, cosmological horizons, and potentially other ordered systems across scales. The paper derives geometric temperature, establishes an information bipartition into structural and dynamic components, and discusses implications for quantum gravity and emergent spacetime. This work is the first in a series exploring the universality of geometric thermodynamics. Authored by an independent researcher.