Synergy as the failure of distributivity
<|reference_start|>Synergy as the failure of distributivity: The concept of emergence, or synergy in its simplest form, is widely used but lacks a rigorous definition. Our work connects information and set theory to uncover the mathematical nature of synergy as the failure of distributivity. It resolves the persistent self-contradiction of information decomposition theory and reinstates it as a primary route toward a rigorous definition of emergence. Our results suggest that non-distributive variants of set theory may be used to describe emergent physical systems.<|reference_end|>
@article{sevostianov2024synergy,
    title={Synergy as the failure of distributivity},
    author={Ivan A. Sevostianov, Ofer Feinerman},
    journal={arXiv preprint arXiv:2404.03455},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.03455},
    primaryClass={cs.IT math.IT physics.bio-ph physics.data-an}
}