Entropy, Expansion, and χ‑Spectral Structuring: Operator‑Geometric Resolution of the Cosmological Order‑from‑Chaos Paradox
Abstract
Recent theoretical developments propose a new interpretation of gravitational dynamics that resolves a long‑standing cosmological paradox: the emergence of increasing structural complexity in an expanding Universe despite the monotonic growth of entropy required by the second law of thermodynamics. Building on the χ‑spectral operator geometry of ZEBTS‑SUPER, we demonstrate that cosmic expansion continuously generates new spectral volume V_chi(t), enabling localized entropy reduction and structure formation without violating global entropy growth (d S_chi / dt >= 0). Gravitational clustering is shown to be an infrared manifestation of χ‑spectral modular dynamics, where local ordering corresponds to the redistribution of entropy into radiation, curvature defects, and χ‑vacuum excitations. This operator‑geometric framework extends general relativity and provides a natural pathway toward a unified quantum theory of gravity.
Related
- Novel geometrical test of cosmological expansion from photometric data
- The Optical Expansion Scalar in Cosmological Perturbation Theory
- AI-assisted super-resolution cosmological simulations V: Cosmology-aware super-resolution
- The environmental dependence of the circumgalactic medium in a high-resolution cosmological simulation
- χ‑Spectral Geometry of Cosmological Mass Renormalization: Operator‑Topological Reconstruction of the Perimeter Institute "Dark Force" Effect
BibTeX
@misc{mukha2026entropy,
title = {{Entropy, Expansion, and χ‑Spectral Structuring: Operator‑Geometric Resolution of the Cosmological Order‑from‑Chaos Paradox}},
author = {Anatolii Mukha},
howpublished = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = jul,
doi = {10.5281/zenodo.21506801},
url = {https://doi.org/10.5281/zenodo.21506801},
note = {CC BY},
}
RIS
TY - UNPB
TI - Entropy, Expansion, and χ‑Spectral Structuring: Operator‑Geometric Resolution of the Cosmological Order‑from‑Chaos Paradox
AU - Anatolii Mukha
PY - 2026
DA - 2026/07/23
PB - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.21506801
UR - https://doi.org/10.5281/zenodo.21506801
AB - Recent theoretical developments propose a new interpretation of gravitational dynamics that resolves a long‑standing cosmological paradox: the emergence of increasing structural complexity in an expanding Universe despite the monotonic growth of entropy required by the second law of thermodynamics. Building on the χ‑spectral operator geometry of ZEBTS‑SUPER, we demonstrate that cosmic expansion continuously generates new spectral volume V_chi(t), enabling localized entropy reduction and structure formation without violating global entropy growth (d S_chi / dt >= 0). Gravitational clustering is shown to be an infrared manifestation of χ‑spectral modular dynamics, where local ordering corresponds to the redistribution of entropy into radiation, curvature defects, and χ‑vacuum excitations. This operator‑geometric framework extends general relativity and provides a natural pathway toward a unified quantum theory of gravity.
ER -