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Beyond Shannon: A Dynamic Model of Entropy in Open Systems
- Entropy is a fundamental concept in various fields, with Shannon entropy commonly used in AI and machine learning to measure uncertainty.
- Traditional static entropy models do not account for dynamic system feedback and entropy stabilization mechanisms in open systems.
- A dynamic entropy model with feedback control was introduced to simulate entropy evolution in a 100-state system.
- The model maintains entropy within a specific range by applying control adjustments based on Shannon entropy computation.
- The Python implementation uses NumPy, SciPy, and Matplotlib to visualize the simulation results.
- Experimental variations include different initial distributions, control gains, transition matrices, and simulation time.
- Results show sensitivity to initial conditions, the impact of control gain on entropy stabilization, and the behavior of structured versus sparse transition matrices.
- Nonlinear adjustments like sinusoidal perturbations lead to small entropy oscillations around the stabilization point.
- The dynamic entropy model highlights the potential for actively controlling entropy in open systems, offering a framework for entropy regulation in AI and probabilistic environments.
- Future work includes applying the model to reinforcement learning, exploring multi-agent entropy dynamics, and extending it to real-world thermodynamic applications.
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