# Onsager’s Non-Equilibrium Thermodynamics as Gradient Flow in Information Geometry

## TL;DR

This paper explores non-equilibrium thermodynamics using gradient flow in information geometry, applying it to ideal and van der Waals gases.

## Contribution

The paper introduces two new gradient-flow models derived from Onsager’s reciprocal relations in the context of information geometry.

## Key findings

- Onsager’s equations can be interpreted as gradient-flow equations under information geometry.
- Two distinct gradient-flow models are developed and compared in their features and relations.
- The models are successfully applied to both ideal and van der Waals gases.

## Abstract

We consider Onsager’s non-equilibrium thermodynamics from the perspective of the gradient flow in information geometry. Assuming Onsager’s reciprocal relations, we can regard his phenomenological equations as gradient-flow equations and develop two different gradient-flow models. We consider their features and their relations. Both models are applied to the ideal gas and van der Waals gas.