Making sense of complex systems through resolution, relevance, and mapping entropy

Roi Holtzman, Marco Giulini, Raffaello Potestio

Published 2022-02-28Version 1

Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those degrees of freedom that mostly determine the behaviour of the system and separate them from less prominent players. Here, we propose an analysis pipeline that integrates three measures of statistical information: resolution, relevance, and mapping entropy. This approach allows one first to identify, in a quantitative manner, the number of degrees of freedom of the system that preserve the largest information content about the generative process that governs it, then to select the specific subset of constituents that optimally provide a synthetic, yet informative reduced representation of the whole. The method, which is implemented in a freely available software, is fully general, as it is shown through the application to three very diverse systems, namely a toy model of independent binary spins, a coarse-grained representation of the financial stock market, and a fully atomistic simulation of a protein.