Statistical thermodynamics and weighted topology of radial networks

TL;DR

This paper introduces a thermodynamic approach using partition functions to analyze and classify radial networks, demonstrated on a model of optimal transport in tree leaves.

Contribution

It presents a novel method linking statistical thermodynamics with weighted topology to characterize radial networks.

Findings

Effective grouping of similar networks based on thermodynamic measures

Application to a model of optimal transport in tree leaves

Provides insights into network development history

Abstract

We propose a method of characterizing radial networks based on a partition function associated with the structural triangulation of the network. The internal energy, Helmholtz free energy, and entropy derived from the partition function are used to group similar networks together and to interrogate the history of their development. We illustrate our methodology for a model for optimal transport in tree leaves.