Thermodynamic forces, flows, and Onsager coefficients in complex networks

TL;DR

This paper applies Onsager's formalism to complex networks, identifying thermodynamic forces and flows resulting from node perturbations, and demonstrates the presence of cross effects similar to thermodiffusion and thermoelectric phenomena.

Contribution

It introduces a novel application of non-equilibrium thermodynamics to complex networks, revealing thermodynamic forces, flows, and cross effects in network responses.

Findings

Thermodynamic forces and flows are induced by node perturbations.

Cross effects like thermodiffusion are observed in networks.

The formalism explains network responses to attacks and removals.

Abstract

We present Onsager formalism applied to random networks with arbitrary degree distribution. Using the well-known methods of non-equilibrium thermodynamics we identify thermodynamic forces and their conjugated flows induced in networks as a result of single node degree perturbation. The forces and the flows can be understood as a response of the system to events, such as random removal of nodes or intentional attacks on them. Finally, we show that cross effects (such as thermodiffusion, or thermoelectric phenomena), in which one force may not only give rise to its own corresponding flow, but to many other flows, can be observed also in complex networks.