# Thermodynamic Theory of Macrosystems: Entropy Production as a Metric

## TL;DR

This paper introduces a thermodynamic model for macrosystems using entropy production as a measure of irreversibility.

## Contribution

The novelty lies in proving that entropy production in a closed macrosystem acts as a metric akin to the Mahalanobis metric.

## Key findings

- Macrosystems can be modeled as self-similar oriented weighted graphs with equations of state at each node.
- Entropy production in stationary processes behaves as a metric indicating irreversibility.
- Onsager’s relations are valid for linear flux-driving force dependencies in such models.

## Abstract

The article considers the description of a macrosystem in terms that do not depend on the nature of the macrosystem. The results obtained can be used to describe macrosystem models of thermodynamic processes, and to create interdisciplinary models that take into account interactions of various natures. The macrosystem model is based on its representation in the form of a self-similar oriented weighted graph where the equation of state is fulfilled for each node, which connects extensive variables. One of the extensive variables is entropy, the maximum of which corresponds to the state of equilibrium. For processes in which fluxes are linearly dependent on driving forces, Onsager’s relations are shown to be true, which makes it possible to prove that in the space of stationary processes, entropy production in a closed macrosystem is a metric similar to the Mahalanobis metric, which determines the distance between processes. Zero in such a space indicates reversible processes, and thus the production of entropy shows the degree of irreversibility as the distance from a researched process to a reversible one.