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Understanding Conditional Independence and Open Systems in Non-Equilibrium Dynamics
Conditional independence within the context of a Markov blanket is distinct from complete independence; it signifies relationships where influences can be distinguished among states rather than suggesting two entirely separate entities. Systems engage in behaviors that reflect this interaction, particularly in terms of their thermal environments, encapsulated in the concept of a heat bath. Open systems are critical in this framework, as they facilitate dynamic exchanges with their environments, allowing internal states to influence external conditions and vice versa. This two-way interaction is essential for understanding self-organization in non-equilibrium dynamics, as such systems operate away from equilibrium states while maintaining defined boundaries between internal and external influences. An illustrative example is provided by single-cell organisms, where intracellular and active states interact with their surroundings, modifying behaviors and properties in response to external stimuli. This intricate interaction preserves conditional independences and lends itself to the application of the renormalization group, highlighting the scaling properties inherent in these non-equilibrium, open systems.
