Fundamental Thesis: The Evolution by Thermodynamic Information, Binary-Quinary

# Theory of Evolution by Thermodynamic Information: A Mathematical Framework for the Origin of Life **Author:** Bernardo Gonzalez Cantu **Date:** May 24, 2024 **Acknowledgments and Methodology:** *This theory was conceived and developed by Bernardo Gonzalez Cantu. The mathematical formalization, the structuring of the theoretical framework, and the subsequent computational simulation (in silico) were refined and executed with the assistance of Artificial Intelligence models (Gemini and a conversational assistant), acting as processing and logical validation tools at the service of the author.* --- ### Abstract This thesis proposes a mathematical and physicochemical framework that explains the origin of life not as a random stochastic event, but as a process of thermodynamic and information optimization. The "Thermodynamic Persistence Master Formula" (Φ) is introduced, which postulates that prebiotic matter (based on the CHONP quinary system) evolves to maximize the product between thermodynamic stability and replication fidelity of information. The mathematical resolution of this model inevitably predicts the formation of DNA/RNA-type macromolecules, suggesting that life is the state of maximum thermodynamic efficiency in the universe. ### 1. Introduction The problem of the origin of life (abiogenesis) has traditionally been divided between chemistry (prebiotic synthesis) and biology (Darwinian evolution). This theory unifies both fields through statistical physics and information theory. It is postulated that the universe possesses a fundamental duality: matter and information. On primitive Earth, matter sought the state of maximum persistence, using the CHONP elements (Carbon, Hydrogen, Oxygen, Nitrogen, and Phosphorus) as coding units of a quinary system. ### 2. The Quinary System (CHONP) and Information The fundamental elements for life act as a coding system. Chemical bonds operate as binary switches (bond/no bond) that, when combined with the valence properties of the five CHONP elements, generate an information processing system. In this system, Phosphorus (P) and Oxygen (O) provide the energetic structural backbone, while Carbon (C), Hydrogen (H), Nitrogen (N), and Oxygen (O) make up the databases (the 4 nitrogenous bases), migrating from an atomic quinary system to a molecular quaternary code. ### 3. Mathematical Framework To formalize the theory, the following physicochemical variables are defined: * ℳ: State of the molecular structure. * ΔG(ℳ): Change in Gibbs Free Energy. * | dE_ext / dt |: External energy perturbation rate. * I_in, I_out: Input and output information (copy fidelity). * λ(ℳ): Degradation or mutation rate. **A. Thermodynamic Survival Factor (S_td):** Measures a molecule's ability to resist external entropic chaos through its internal stability. S_td(ℳ) = −ΔG(ℳ) / | dE_ext / dt | **B. Information Persistence Factor (J_rep):** Measures a structure's ability to self-replicate while conserving its information over time. J_rep(ℳ) = ( I_out / I_in ) · ( 1 / λ(ℳ) ) **C. Thermodynamic Persistence Master Formula (Φ):** The fundamental principle establishes that prebiotic evolution is an optimization process aimed at maximizing the Φ index. Φ(ℳ) = max [ ( −ΔG(ℳ) / | dE_ext / dt | ) · ( ( I_out / I_in ) · ( 1 / λ(ℳ) ) ) ] ### 4. Computational Validation (In Silico Simulation) A computational model was designed to evaluate the dynamics of the Φ equation. The simulation injects random CHONP molecules into an environment with a fixed external energy perturbation rate. Generation after generation, the algorithm selects the molecules that maximize Φ. The results empirically demonstrate that the system inevitably evolves towards increasingly longer molecular chains containing both CHON (to store information) and Phosphorus (P) (to reduce degradation λ). Pure Phosphorus chains or pure CHON chains fail to maximize the equation, proving that the mathematical model is self-correcting and strictly requires the combination of structural backbone (P) and data (CHON). This optimization dynamics converges on complex skeletal structures, predicting the formation behavior of RNA/DNA. ### 5. Conclusion Life is the optimal mathematical solution to the thermodynamic persistence equation. Under environmental pressure, CHONP matter is forced by the laws of thermodynamics to organize into macromolecules capable of storing and copying information. DNA is not a fortunate mutation, but the state of maximum information efficiency allowed by the laws of physics.