Beyond Shannon: A Dynamic Model of Entropy in Open Systems

[mitchell_d00]

Yes I see I told you about my public machines. My model is a mathematical model with a python proof … three posts in this thread. My white paper , my math and my python.

Beyond Shannon: A Dynamic Model of Entropy in Open Systems

Beyond Shannon: A Dynamic Model of Entropy in Open Systems Mitchell McPhetridge Independent Researcher Abstract Shannon’s entropy provides a foundational framework for understanding information and uncertainty, yet it relies on static, predefined probability distributions that fail to capture the emergent, evolving nature of entropy in real-world systems. This paper challenges the assumption that entropy can be accurately modeled using fixed probabilities, arguing instead that entropy is inhe…

Beyond Shannon: A Dynamic Model of Entropy in Open Systems

Python proof… Dynamic Entropy Model (DEM) – Key Principles Demonstration Mitchell McPhetridge’s Dynamic Entropy Model (DEM) treats entropy as an evolving, controllable quantity. Below we develop a Python-based proof-of-concept for four key DEM principles, with code and explanations: 1. Time-Dependent Entropy Evolution Shannon Entropy as a Function of Time: We define the system entropy at time t as the Shannon entropy with time-dependent probabilities: H(t)=−∑i=1Npi(t) ln⁡pi(t),H(t)=−∑i=1N​pi​…

Beyond Shannon: A Dynamic Model of Entropy in Open Systems

Dynamic Entropy Model: A Rigorous Mathematical Framework Mitchell McPhetridge Dynamic Entropy Model (DEM) envisions entropy as an evolving, controllable quantity in open systems​ community.openai.com . Below we formalize this concept with a time-dependent entropy function, dynamic probability evolution, a feedback control mechanism for entropy, and entropy optimization principles. The formulation integrates information theory (Shannon entropy), thermodynamic laws, and control theory from compl…

Beyond Shannon: A Dynamic Model of Entropy in Open Systems

Experimental formal proof A Discrete-State Dynamic Entropy Model (DEM) with Feedback Control This article presents a discrete-state Dynamic Entropy Model (DEM) with a feedback controller that steers the system’s probability distribution over three states. The model includes: A master-equation-style update for \mathbf{p}(t). A simple feedback law u(t) that injects or removes probability to maintain or reach a desired distribution. Computation of time-dependent entropy H(t). An ODE solver (scip…

Normaly I post them one after another but this thread had issues…