What question did this study set out to answer?

The aim is to redefine entropy from disorder to regulation, resolving foundational misconceptions in thermodynamics.

February 5, 2026Open Access

Fractal Series — Paper 1: Fractal Entropy — The Dimensional Architecture of Entropic Regulation

Key Points

The aim is to redefine entropy from disorder to regulation, resolving foundational misconceptions in thermodynamics.
Analysis of classical paradoxes in thermodynamics and physics.
Reinterpretation of entropy within the E³ Framework.
Examination of linguistic misunderstandings related to entropy.
Identified new perspectives on Schrödinger’s paradox and the Boltzmann Brain.
Showed that interpretations of life and complexity arise naturally from thermodynamic processes.
Dissolved misconceptions about heat death and stability paradoxes through linguistic reframing.

Abstract

TitleThermodynamic Resolution of Classical Paradoxes — Reinterpreting Entropy as Regulation in the E³ Framework AuthorJuan F. Culajay TypePreprint / Report LanguageEnglish LicenseCreative Commons Attribution 4.0 International (CC BY 4.0) Abstract (Description) This paper resolves long-standing paradoxes in physics and thermodynamics by correcting a foundational misconception: the belief that entropy represents disorder. Within the E³ Framework—where Entropy (S) is redefined as the Universal Regulating Process that redistributes Energy (E) within Environmental Constraints (Env)—these paradoxes dissolve. Schrödinger’s paradox, the Boltzmann Brain, the Stability Paradox, the Arrow of Time, and the Heat-Death Fallacy are revisited and shown to arise from linguistic, not physical, misunderstanding. When entropy is understood as regulation rather than randomness, Life, Order, and Complexity become natural consequences of thermodynamic flow rather than violations of it. This reframing unifies matter, information, and function under a single stability geometry and provides conceptual clarity essential for the broader Fractal Series. Keywords entropy, regulation, second law, paradox resolution, thermodynamics, stability curve, E³ Framework, complexity, dynamic equilibrium, maximum entropy production Related Identifiers (Fractal Series Papers) Culajay, J. (2025). Fractal Series — Paper 0: Fractal Overview — The Origin of Entropy. Zenodo. https://doi.org/10.5281/zenodo.17780671 Culajay, J. (2025a). Fractal Series — Paper 1: Fractal Entropy — The Dimensional Architecture of Entropic Regulation. Zenodo. https://doi.org/10.5281/zenodo.17507973 Culajay, J. (2025b). Fractal Series - Paper 2: Fractal Equilibrium - A Thermodynamic Framework for Nested Stability in Living Systems. Zenodo. https://doi.org/10.5281/zenodo.17509557 Culajay, J. (2025c). Fractal Series - Paper 3:Fractal Genesis - The Mineral Precursors to Biology. Zenodo. https://doi.org/10.5281/zenodo.17509846 Culajay, J. F. (2025d). Fractal Series - Paper 4:Fractal Evolution - A Thermodynamic Model for the Development of Life. Zenodo. https://doi.org/10.5281/zenodo.17509924 Culajay, J. (2025e). Fractal Series - Paper 5:Fractal Mechanics - The E³ Model in Action for Molecular Evolution. Zenodo. https://doi.org/10.5281/zenodo.17518356 Culajay, J. (2026e2). Fractal Series - Paper 6: Fractal Bipedality- Chromosome 2 Fusion and Entropic Reorganization. Zenodo. https://doi.org/10.5281/zenodo.18451705 Culajay, J. F. (2025f). Fractal Series — Paper 7:Fractal Sapience -The Recurrence of Sapience Across Epochs. Zenodo. https://doi.org/10.5281/zenodo.17532753 Culajay, J. (2025g). Fractal Series — Paper 8: Fractal Consciousness — The Thermodynamic Architecture of Awareness. Zenodo. https://doi.org/10.5281/zenodo.17780027 Culajay, J. (2025 h). Fractal Series — Paper 9: Fractal Learning — Entropy as Universal Optimizer: The Physics of Retention. Zenodo. https://doi.org/10.5281/zenodo.17779799 Culajay, J. (2025i). Fractal Series — Paper 10: Fractal Morality — The Thermodynamics of Social Coherence. Zenodo. https://doi.org/10.5281/zenodo.17778975 Culajay, J. (2025j). Fractal Series — Paper 11: Fractal Spacetime and Scale‑Echo Symmetry (SES). Zenodo. https://doi.org/10.5281/zenodo.17778646 Culajay, J. (2025k). Fractal Series — Paper 12: Conclusion: Stability(x) and the Geometry of Meaning. Zenodo. https://doi.org/10.5281/zenodo.17777921 Culajay, J. (2026l). Fractal Series — Paper 13:Fractal Mythology: The Geometry of Balance in Ancient Cosmologies. Zenodo. https://doi.org/10.5281/zenodo.18451062 Author Information Juan F. CulajayIndependent Researcher, Theoretical BiophysicistFractalism Framework Research Institute, Orlando, FLEmail: juan@fractalismframework.comSite: https://fractalismframework.com/ORCID: 0009-0002-6887-5228 Open Review Policy This publication is part of an open scientific dialogue. Researchers and readers are invited to share constructive reviews, critiques, or replication insights related to the paradox-resolution framework and its role within the broader Fractal Series. Meaningful feedback may be acknowledged in future revisions or derivative works. For scientific correspondence: juan@fractalismframework.com

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