Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A Graph-Theoretic Approach to Understanding Emergent Behavior in Physical Systems

Version 1 : Received: 11 February 2021 / Approved: 12 February 2021 / Online: 12 February 2021 (11:11:50 CET)

How to cite: Adams, A. A Graph-Theoretic Approach to Understanding Emergent Behavior in Physical Systems. Preprints 2021, 2021020299 (doi: 10.20944/preprints202102.0299.v1). Adams, A. A Graph-Theoretic Approach to Understanding Emergent Behavior in Physical Systems. Preprints 2021, 2021020299 (doi: 10.20944/preprints202102.0299.v1).

Abstract

The exact dynamics of emergence remains one of the most prominent outstanding questions for the field of complexity science. I first discuss various perspectives on emergence in various contexts, then offer a different perspective on understanding emergence in a graph-theoretic representation. From the discussion, an observer’s choice in state space seems to have an effect for that observer to detect emergent behavior. To test these ideas, I analyze the dynamics of all possible spatial state spaces near the critical temperature in an Ising model. As a result, state space topologies that appear more deterministic flip more bits than topologies that appear more random, which is contrary to our intuitions about randomness. In addition, the size of different state spaces constrain a system’s ability to explore various states within the same time frame. These results are important to understanding emergent phenomena in biological systems, which are layered with various state spaces and observational perspectives.

Subject Areas

Emergence; Ising Model; Information; Computation; State Space

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