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Stochastic Chaos and Markov Blankets.

Karl Friston1, Conor Heins2,3,4, Kai Ueltzhöffer1,5

  • 1Wellcome Centre for Human Neuroimaging, Institute of Neurology, University College London, London WC1N 3AR, UK.

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|September 28, 2021
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We identified conditional independencies in nonequilibrium steady-state systems, partitioning states using Markov blankets. This reveals a physics of sentience where internal states infer external states through chaotic synchronisation.

Keywords:
BayesianMarkov blanketinformation geometrythermodynamicsvariational inference

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Area of Science:

  • Statistical physics
  • Dynamical systems theory
  • Information theory

Background:

  • Conditional independencies are crucial for understanding complex systems, particularly in nonequilibrium steady states.
  • Existing research lacks established methods for identifying partitions that isolate internal states from external influences.
  • The information geometry of internal states suggests potential links to sentience, but requires empirical validation.

Purpose of the Study:

  • To establish the existence and identification of conditional independencies in nonequilibrium steady states.
  • To explore the implications of these independencies for the information geometry of internal states and sentience.
  • To develop a mathematical framework for understanding the coupling between internal and external states.

Main Methods:

  • Utilizing the Lorenz system as a model for stochastic chaos.
  • Employing Helmholtz decomposition and polynomial expansions to parameterize the steady-state density.
  • Leveraging the Hessian matrix to identify Markov blankets and characterize state coupling.

Main Results:

  • Demonstrated the parameterization of steady-state density using surprisal or self-information.
  • Showcased the identification of Markov blankets for state partitioning.
  • Characterized the coupling between internal and external states via generalized synchrony or chaotic synchronization.

Conclusions:

  • The identified partitions and their functional forms provide a basis for understanding information flow in complex systems.
  • Generalized synchrony offers a potential mathematical foundation for elemental forms of sentience in biological systems.
  • This work bridges concepts from statistical physics, dynamical systems, and information theory to explore the emergence of sentience.