A simplified climate model and maximum entropy production

TL;DR

This paper revisits a simplified climate model based on maximum entropy production, providing an analytical solution that confirms the extremum is a maximum, clarifying theoretical debates in thermodynamics.

Contribution

It offers an analytical solution to the variational principle in a simplified climate model, demonstrating the extremum is a maximum, thus addressing controversy in entropy production theories.

Findings

Analytical solution to the Euler-Lagrange equation for the model

Confirmation that the extremum is a maximum entropy production

Clarification of the thermodynamic controversy

Abstract

A simplified climate model based on maximum entropy production, described by a variational principle, is revisited and an analytical solution to its Euler-Lagrange equation is found. Mindful of controversy about maximum or minimum entropy production in open thermodynamical systems, we show that the solution extremizing the action integral corresponds to a maximum.