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

Roi Holtzman1, Marco Giulini2,3, and Raffaello Potestio2,3,*

  • 1Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
  • 2Physics Department, University of Trento, via Sommarive, 14 I-38123 Trento, Italy
  • 3INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, I-38123 Trento, Italy

  • *raffaello.potestio@unitn.it
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Phys. Rev. E 106, 044101 – Published 3 October, 2022

DOI: https://doi.org/10.1103/PhysRevE.106.044101

Abstract

Complex systems are characterized by a tight, nontrivial interplay of their constituents, which gives rise to a multiscale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those degrees of freedom that mostly determine the behavior of the system and separate them from less prominent players. Here, we tackle this problem making use of three measures of statistical information: Resolution, relevance, and mapping entropy. We address the links existing among them, taking the moves from the established relation between resolution and relevance and further developing novel connections between resolution and mapping entropy; by these means we can identify, in a quantitative manner, the number and selection of degrees of freedom of the system that preserve the largest information content about the generative process that underlies an empirical dataset. 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.

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Phys. Rev. E 106, 044101– Published 3 October, 2022
  • Received 2 March 2022
  • Accepted 16 August 2022
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