Umbilic Thermodynamics

 https://vasil7penchev.wordpress.com/wp-content/uploads/2026/08/umbilic-thermodynamics-2.pdf

Abstract:This paper develops umbilic thermodynamics, a generalized thermodynamic framework based on the conservation

of dimensionless, scale-invariant Weyl information across a non-orientable Möbius topology. Within a conformal

projective geometric algebra (PGA) formulation, probability-distribution shapes and pseudo-Riemannian metric

shapes are interpreted as grade-dual projections of a single underlying structure, linking microscopic phase

entropy with macroscopic metric stress-energy. A corresponding Weyl temperature is introduced to characterize

the conversion between these informational and geometric manifestations. The framework formulates four

principles of umbilic thermodynamics concerning symplectic-capacity equilibrium, global Weyl-information

conservation, topological entropy directionality, and the unattainability of global absolute zero. A singular

Legendre transformation at the Gromov symplectic boundary provides a local “backdoor” through which

phase-space compression and negative informational temperatures can produce localized metric stress-energy,

while global Weyl-information conservation prohibits net creation ex nihilo. The resulting generalized umbilic

ergodic theorem identifies local “creatio ex nihilo” events as recurrent, measure-preserving transfers between

dual phase sheets. Classical thermodynamics and quantum thermodynamics are recovered as limiting projections

of the generalized framework, while a statistical formulation is developed in Boltzmannian, Gibbsian, and

Einsteinian editions. The paper further proposes falsifiable experimental tests involving entangled quantum

systems, cryogenic cavities, superconducting qubits, and non-orientable photonic structures. Thus, umbilic

thermodynamics is presented as a unified topodynamical framework connecting information, entropy, quantum

phase structure, spacetime curvature, and thermodynamic evolution.

Keywords:umbilic thermodynamics; Weyl information; Weyl temperature; conformal projective geometric algebra;

Möbius topology; non-orientable manifold; Legendre transformation; Gromov symplectic capacity;

phase entropy; negative temperature; informational temperature; creatio ex nihilo; metric stress-energy;

generalized ergodic theorem; topodynamical dynamics; quantum thermodynamics; statistical thermodynamics;

quantum entanglement; spacetime curvature; thermodynamic duality.