Information Content and Maximum Entropy of Compartmental Systems in Equilibrium

Abstract

Mass-balanced compartmental systems defy classical deterministic entropy measures since both metric and topological entropy vanish in dissipative dynamics. By interpreting open compartmental systems as absorbing continuous-time Markov chains that describe the random journey of a single representative particle, we allow established information-theoretic principles to be applied to this particular type of deterministic dynamical system. In particular, path entropy quantifies the uncertainty of complete trajectories, while entropy rates measure the average uncertainty of instantaneous transitions. Using Shannon's information entropy, we derive closed-form expressions for these quantities in equilibrium and extend the maximum entropy principle (MaxEnt) to the problem of model selection in compartmental dynamics. This information-theoretic framework not only provides a systematic way to address equifinality but also reveals hidden structural properties of complex systems such as the global carbon cycle.

Keywords

information entropy; compartmental systems; equifinality; model identification; MaxEnt; reservoir models

Published in

Entropy
2025, volume: 27, number: 10, article number: 1085
Publisher: MDPI

SLU Authors

• Metzler, Holger

  • Department of Forest Ecology and Management, Swedish University of Agricultural Sciences
    
  • Department of Crop Production Ecology, Swedish University of Agricultural Sciences
    
  • Ludwig Maximilian University Munich (LMU)
  • Max Planck Institute for Biogeochemistry

UKÄ Subject classification

Statistical physics and complex systems
Geosciences, Multidisciplinary

Publication identifier

• DOI: https://doi.org/10.3390/e27101085

Permanent link to this page (URI)

https://res.slu.se/id/publ/144593