# Entropy production and fluctuation theorems on complex networks

## TL;DR

This paper investigates entropy production in complex networks by analyzing data packet transport, deriving exact EP distributions along shortest paths, and revealing that the asymptotic distribution follows a Gumbel distribution.

## Contribution

It introduces a novel approach to quantify entropy production in complex networks using shortest path analysis and extreme value theory, revealing the Gumbel distribution as the asymptote.

## Key findings

- EP distribution along shortest paths is exactly enumerated.
- The asymptote of the EP distribution follows a Gumbel distribution.
- Complex pathways significantly influence entropy production.

## Abstract

Entropy production (EP) is known as a fundamental quantity for measuring the irreversibility of processes in thermal equilibrium and states far from equilibrium. In stochastic thermodynamics, the EP becomes more visible in terms of the probability density functions of the trajectories of a particle in the state space. Inspired by a previous result that complex networks can serve as state spaces, we consider a data packet transport problem on complex networks. Entropy is produced owing to the complexity of pathways as the packet travels back and forth between two nodes. The EPs are exactly enumerated along the shortest paths between every pair of nodes, and the functional form of the EP distribution is determined by extreme value analysis. The asymptote of the accumulated EP distribution is found to follow the Gumbel distribution.