Physical Review Research, Journal Year: 2025, Volume and Issue: 7(2)
Published: April 7, 2025
Relating macroscopic observables to microscopic interactions is a central challenge in the study of complex systems. While current approaches often focus on pairwise interactions, complete understanding requires going beyond these capture full range possible interactions. We present unified mathematical formalism, based Möbius inversion theorem, that reveals how different decompositions system into parts lead different, but equally valid, theories. By providing an exact bridge between and descriptions, this framework demonstrates many existing notions interaction, from epistasis genetics many-body couplings physics, synergy game theory artificial intelligence, naturally uniquely arise particular choices decomposition, or . revealing common structure underlying seemingly disparate phenomena, our paper highlights choice decomposition fundamentally determines nature resulting discuss unifying perspective can facilitate transfer insights across domains, guide selection appropriate decompositions, enable search for new interaction. To illustrate latter practice, we decompose Kullback-Leibler divergence, show method correctly identifies which variables are responsible divergence. In addition, use Rota's Galois connection theorem describe coarse grainings mereologies, efficiently derive renormalized 1D Ising model. Our results suggest provides powerful practical lens emergence behavior interplay parts, with applications wide disciplines. Published by American Physical Society 2025
Language: Английский