Stochastic cycle selection in active flow networks

TL;DR

This paper develops a theoretical framework combining lattice field theory, graph theory, and transition rate theory to understand how network topology influences flow cycle selection in active flow networks, with broad applications.

Contribution

It introduces symmetry-based rules that classify and predict flow cycle statistics from network topology in active, non-equilibrium networks.

Findings

Identifies symmetry principles governing flow cycle selection.

Establishes a connection between active flow networks and ice-type models.

Provides a predictive framework for flow statistics based on network topology.

Abstract

Active biological flow networks pervade nature and span a wide range of scales, from arterial blood vessels and bronchial mucus transport in humans to bacterial flow through porous media or plasmodial shuttle streaming in slime molds. Despite their ubiquity, little is known about the self-organization principles that govern flow statistics in such non-equilibrium networks. Here we connect concepts from lattice field theory, graph theory, and transition rate theory to understand how topology controls dynamics in a generic model for actively driven flow on a network. Our combined theoretical and numerical analysis identifies symmetry-based rules that make it possible to classify and predict the selection statistics of complex flow cycles from the network topology. The conceptual framework developed here is applicable to a broad class of non-biological far-from-equilibrium networks, including actively controlled information flows, and establishes a new correspondence between active flow networks and generalized ice-type models.