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The Universal Stability Law: A Unified Framework for Nonlinear Pattern Formation and Stability Transitions

Authors: Muñoz Rodriguez, Jonatan;

The Universal Stability Law: A Unified Framework for Nonlinear Pattern Formation and Stability Transitions

Abstract

The Universal Law of Descent (LUDC) establishes a physical bound on the rate of entropy reduction in computational and self-organizing systems: **Equation:** −dS/dt ≤ κ · C(t) · P(t) where C(t) represents structural conductance and P(t) operational power.Extending the Universal Stability Law (USL), the LUDC unifies informational geometry, stochastic thermodynamics, and computational complexity, providing a measurable physical constraint on the ordering rate of systems — from combinatorial algorithms (SAT, TSP) to dynamical models (machine learning, sandpile automata). Simulations across domains show less than 5% deviation from the theoretical bound, suggesting that entropy reduction — and thus computational efficiency — is limited by universal energetic constraints. This work bridges the physics of information and the foundations of complexity theory, offering an experimentally testable perspective on the P vs NP problem.

Establishes the Universal Law of Descent (LUDC), a physical bound on the rate of entropy reduction in computational and self-organizing systems (−dS/dt ≤ κ·C·P). Extends the Universal Stability Law (USL), linking information geometry, thermodynamics, and computational complexity with measurable implications for the P vs NP problem.

Keywords

computation, USL, LUDC, stability, bounded attractors, neural networks, power grids, phase diagram, information, limited propagation, nonlinear dynamics, pattern formation, networks, Information, bifurcation, Thermodynamics, universality, complex systems, ecosystems, entropy, synchronization, universal stability law, stability transitions, P vs NP

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
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