# From Maximum Entropy to Maximum Entropy Production: A New Approach

## Abstract

**:**

## 1. Introduction

## 2. Background: The Maximum Entropy Production Principle and Some Open Problems

#### 2.1. An Example: Two-Box Atmospheric Models

**Figure 1.**A diagram showing the components of the two-box atmospheric heat transport model. Labels written next to arrows indicate rates of flow of energy, whereas labels in boxes represent temperature.

#### 2.2. Generalisation: Negative Feedback Boundary Conditions

#### 2.3. The System Boundary Problem

#### 2.4. Some Comments on Dewar’s Approach

## 3. Thermodynamics as Maximum Entropy Inference

#### 3.1. A New Argument for the MEPP

#### 3.2. Application to the Steady State with a Fixed Gradient

## 4. A Possible Solution to the System Boundary Problem

**Figure 2.**Two possible ways in which negative feedback boundary conditions could be realised. $\left(a\right)$ Heat flows into $\mathrm{A}$ from a much larger reservoir ${\mathrm{A}}^{\prime}$, and out of $\mathrm{B}$ into another large reservoir ${\mathrm{B}}^{\prime}$. $\left(b\right)$ A reversible heat engine is used to extract power by transferring heat between two external reservoirs ${\mathrm{A}}^{\u2033}$ and ${\mathrm{B}}^{\u2033}$, and this power is used to transfer heat reversibly out of $\mathrm{B}$ and into $\mathrm{A}$. In this version the only entropy produced is that produced inside $\mathrm{C}$ due to the heat flow Q.

#### 4.1. Application to Atmospheres and Other Systems

## 5. Discussion

#### 5.1. The Need for Experimental Study

#### 5.2. The Relationship Between Thermodynamics and Kinetics

## 6. Conclusions

## Acknowledgements

## References

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**MDPI and ACS Style**

Virgo, N.
From Maximum Entropy to Maximum Entropy Production: A New Approach. *Entropy* **2010**, *12*, 107-126.
https://doi.org/10.3390/e12010107

**AMA Style**

Virgo N.
From Maximum Entropy to Maximum Entropy Production: A New Approach. *Entropy*. 2010; 12(1):107-126.
https://doi.org/10.3390/e12010107

**Chicago/Turabian Style**

Virgo, Nathaniel.
2010. "From Maximum Entropy to Maximum Entropy Production: A New Approach" *Entropy* 12, no. 1: 107-126.
https://doi.org/10.3390/e12010107