Extrinsic vs Intrinsic Criticality in Systems with Many Components

• Type of Material: Article
• Authors: Vudtiwat Ngampruetikorn, City University of New York; Ilya Nemenman, Emory University; David J. Schwab, City University of New York
• Language: English
• Date: 2023-09-25
• Publisher: Cornell University
• Publication Version: Preprint (Prior to Peer Review)
• Copyright Statement: © Cornell University 2023
• Final Published Version (URL): https://doi.org/10.48550/arXiv.2309.13898
• Title of Journal or Parent Work: arXiv
• Start Page: 13898v1
• Grant/Funding Information: VN and DJS acknowledge support from the National Science Foundation, through the Center for the Physics of Biological Function (PHY-1734030). DJS is supported in part by the Simons Foundation and by the Sloan Foundation. IN was supported in part by the Simons Foundation Investigator grant and the NIH grants 1R01NS099375 and 2R01NS084844.
• Keywords: Intrinsic criticality; atypically large correlated fluctuations; Extrinsic criticality
• Research Categories: Physics, General

Abstract

Biological systems with many components often exhibit seemingly critical behaviors, characterized by atypically large correlated fluctuations. Yet the underlying causes remain unclear. Here we define and examine two types of criticality. Intrinsic criticality arises from interactions within the system which are fine-tuned to a critical point. Extrinsic criticality, in contrast, emerges without fine tuning when observable degrees of freedom are coupled to unobserved fluctuating variables. We unify both types of criticality using the language of learning and information theory. We show that critical correlations, intrinsic or extrinsic, lead to diverging mutual information between two halves of the system, and are a feature of learning problems, in which the unobserved fluctuations are inferred from the observable degrees of freedom. We argue that extrinsic criticality is equivalent to standard inference, whereas intrinsic criticality describes fractional learning, in which the amount to be learned depends on the system size. We show further that both types of criticality are on the same continuum, connected by a smooth crossover. In addition, we investigate the observability of Zipf’s law, a power-law rank-frequency distribution often used as an empirical signature of criticality. We find that Zipf’s law is a robust feature of extrinsic criticality but can be nontrivial to observe for some intrinsically critical systems, including critical mean-field models We further demonstrate that models with global dynamics, such as oscillatory models, can produce observable Zipf’s law without relying on either external fluctuations or fine tuning. Our findings suggest that while possible in theory, fine tuning is not the only, nor the most likely, explanation for the apparent ubiquity of criticality in biological systems with many components. Our work offers an alternative interpretation in which criticality, specifically extrinsic criticality, results from the adaptation of collective behavior to external stimuli.