ENTROPIC EFFICIENCY DYNAMICS

ENTROPIC EFFICIENCY DYNAMICS (EED) Unified Framework of Computational Physics, Emergent Gravity, and Complex SystemsVERSION: 5.3 (Hard Science Edition - Peer Review) AUTHOR: IVAN ERICK TLALTECATL MORALES AFFILIATION: Independent Researcher in Information Physics DATE: January, 2026 (03 2026 010812130000 1)I. ABSTRACT This paper proposes Entropic Efficiency Dynamics (EED) as a theoretical framework to resolve the incompatibility between General Relativity and Quantum Mechanics. We postulate that spacetime is not a fundamental continuum, but an emergent property of a discrete Causal Set, governed by principles of computational resource optimization ("Lazy Evaluation"). The model derives gravity as an entropic force from the Fisher Information Metric and redefines inertial mass as the local state update frequency (f = mc^2 / h). A stress-based interferometry experimental protocol is proposed to detect the dynamic granularity of the vacuum, and the measurement problem is discussed from an information theory perspective.II. INTRODUCTION: LIMITATIONS OF INFINITE RESOURCE MODELS Standard cosmological models implicitly assume an infinite information processing capacity to define physical variables in the continuum. This assumption leads to mathematical singularities in General Relativity and the measurement problem in Quantum Mechanics.EED addresses these inconsistencies by quantizing computational action, suggesting that physical reality is defined solely through direct causal interaction, keeping unobserved states in latent superposition to minimize the global entropy of the system.III. DISCRETE SPACETIME FORMALISM3.1. Stochastic Causal Sets Spacetime is modeled as a locally finite Causal Set (C). To preserve statistical Lorentz Invariance, the distribution of events follows a Poisson process ("Sprinkling"):P(N) = [ (ρ * V)^N * e^(-ρ * V) ] / N!Where "ρ" (rho) is the discreteness density at the Planck scale.3.2. Gravity as an Entropic Gradient The spacetime metric is derived from the Fisher Information Metric. Gravity is not postulated as a fundamental force, but as an emergent phenomenon derived from the maximization of Shannon entropy on the holographic screen.The force (F) arises thermodynamically:F = T * (∇S)Where an increase in information density (matter) reduces local degrees of freedom, generating an effective "attraction" to minimize processing cost (∇S is the entropy gradient).IV. INFORMATION DYNAMICS AND THERMODYNAMICS4.1. Mass-Frequency Equivalence We propose the unification of mass-energy equivalence and the Planck relation via the master equation:f_local = (m * c^2) / hMass (m) is reinterpreted as the computational refresh rate necessary to maintain the coherence of a localized quantum state.4.2. Minimum Update Principle (Inertia) Inertia is defined as the system's resistance to algorithmic state changes. Inertial trajectories correspond to geodesics of minimum computational cost in the causal graph. Acceleration implies an active rewriting of causal neighborhood relations, which entails an associated energetic cost.4.3. Vacuum Thermodynamics (Lazy Evaluation) The universe operates under a "Lazy Evaluation" scheme, computing physical states only upon causal demand. This implies that the quantum vacuum does not possess infinite energy density, but acts as a latent information reservoir with minimal entropy until perturbed. Monte Carlo simulations suggest this model is thermodynamically more stable than continuous evaluation models, with an efficiency exceeding 98%.V. EXPERIMENTAL EVIDENCE AND COMPUTATIONAL VALIDATION5.1. Dynamic Holographic Noise and the Stress Coefficient We address the discrepancy with the negative results of the "Holometer" experiment (Fermilab). Under EED, holographic noise (S_h) is not a static background, but a variable dependent on local processing activity. We introduce the Computational Stress Coefficient (ξ):S_h ≈ ξ(I) * √( L * l_planck )Where ξ(I) (xi) tends to 0 in the vacuum (explaining previous null results) and tends to 1 in regions of high energy density.Proposed Experimental Protocol: Differential Michelson interferometry where one of the optical arms is subjected to a high-intensity magnetic field or proximity to dense mass ("Stress Test"). A phase coherence loss correlated solely in the stressed arm is predicted.5.2. Numerical Validation A high-fidelity comparative simulation was performed using Monte Carlo methods to contrast the Classical Model (Eager Evaluation) against the EED Model (Lazy Evaluation). Results showed that the Standard Model's energy consumption scales linearly with N (making it unfeasible at large scales), while the EED Model presentslogarithmic consumption, suggesting that EED acts as a thermodynamic attractor for cosmic stability.VI. THE MEASUREMENT PROBLEM IN COMPUTATIONAL SYSTEMS From an information theory perspective, the "Observer" requires no metaphysical or biological properties but is strictly defined as a measurement system capable of establishing a quantum correlation (entanglement) with the observed system.Following the principles of Von Neumann and Shannon, wavefunction collapse is interpreted as a memory optimization operation: the system transitions from a complex probability distribution (superposition) to a defined eigenvalue (classical bit) only when necessary to resolve a causal inconsistency. This "Collapse on Demand" mechanism minimizes the global Kolmogorov entropy of the system, eliminating the need to calculate unobserved historical trajectories and resolving the Schrödinger's Cat paradox through pure algorithmic efficiency.VII. MATHEMATICAL DISCUSSION: TOPOLOGICAL CONJECTURE As an additional theoretical consideration, we note that the fine-structure constant (α) can be approximated via the volume of bounded symmetric spaces (Wyler, 1971). If we model the information phase space as a D5 domain and physical space as S4, we obtain:α ≈ 1 / 137.036While we acknowledge this is a geometric approximation and not a complete dynamic derivation, we suggest that coupling constants could emerge from topological constraints in information projection between manifolds of different dimensions—a hypothesis deserving exploration independent of the main dynamics presented here.VIII. CONCLUSION Entropic Efficiency Dynamics offers a parsimonious framework unifying gravitational and quantum phenomenology via information theory. By introducing fundamental discreteness and on-demand evaluation, classical singularities are eliminated, and a causal explanation for wavefunction collapse based on thermodynamics is offered. The critical validation of this model lies in the experimental detection of stress-induced holographic noise, which would establish the computational nature of physical reality.IX. SELECTED REFERENCES1. Bombelli, L., et al. (1987). "Space-time as a causal set". Phys. Rev. Lett.2. Shannon, C. E. (1948). "A Mathematical Theory of Communication". Bell System Technical Journal.3. 't Hooft, G. (1993). "Dimensional Reduction in Quantum Gravity". arXiv:gr-qc.4. Lloyd, S. (2002). "Computational capacity of the universe". Phys. Rev. Lett.5. Verlinde, E. (2011). "On the Origin of Gravity and the Laws of Newton". JHEP.