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Information Content and Maximum Entropy of Compartmental Systems in Equilibrium
Holger Metzler1,2,3,4, Carlos A Sierra1
1Max Planck Institute for Biogeochemistry, Hans-Knöll-Str. 10, 07745 Jena, Germany.
This study applies information theory to mass-balanced compartmental systems, using Markov chains to quantify trajectory uncertainty and transitions. This approach reveals system structures and aids model selection, overcoming limitations of classical entropy measures.
Area of Science:
- Complex Systems
- Information Theory
- Statistical Mechanics
Background:
- Classical entropy measures fail for mass-balanced compartmental systems with dissipative dynamics.
- Open compartmental systems are reinterpreted as absorbing continuous-time Markov chains.
Purpose of the Study:
- To apply information-theoretic principles to deterministic dynamical systems.
- To quantify trajectory uncertainty and transition uncertainty in compartmental systems.
- To extend the maximum entropy principle for model selection.
Main Methods:
- Interpreting compartmental systems as continuous-time Markov chains.
- Applying Shannon's information entropy to derive path entropy and entropy rates.
- Deriving closed-form expressions for these quantities in equilibrium.
Main Results:
- Developed a novel information-theoretic framework for compartmental dynamics.
- Derived closed-form expressions for path entropy and entropy rates.
- Extended the maximum entropy principle (MaxEnt) for model selection.
Conclusions:
- The framework systematically addresses equifinality in compartmental models.
- Reveals hidden structural properties of complex systems, like the global carbon cycle.
- Offers a new perspective on analyzing deterministic dynamical systems.
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