# Ensembles of Atoms, Ensembles of Species: Comparative Statistical Mechanics

## Abstract

**:**

## 1. Introduction

## 2. Microcanonical Ensembles

#### 2.1. The Classical Perfect Gas

#### 2.2. Alien Species

## 3. Dynamics

#### 3.1. Atomic Collisions

#### 3.2. Species Master Equations

#### 3.3. Species Collisions?

#### 3.4. A Diversion into Population Dynamics

#### 3.5. Atoms—The Master Equation?

## 4. Discussion

## Funding

## Conflicts of Interest

## References

- Kelly, C.K.; Blundell, S.J.; Bowler, M.G.; Fox, G.A.; Harvey, P.H.; Lomas, M.R.; Ian Woodward, F. The statistical mechanics of community assembly and species distribution. New Phytol.
**2011**, 191, 819–827. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bowler, M.G.; Kelly, C.K. On the statistical mechanics of alien species distribution. Entropy
**2017**, 19, 674. [Google Scholar] [CrossRef] [Green Version] - MacArthur, R.H. On the relative abundance of species. Am. Nat.
**1960**, 94, 25–36. [Google Scholar] [CrossRef] - Blundell, S.J.; Blundell, K.M. Thermal Physics; Oxford University Press: Oxford, UK, 2006. [Google Scholar]
- Bowler, M.G. Lectures on Statistical Mechanics; Pergamon Press: Oxford, UK, 1982. [Google Scholar]
- Bowler, M.G. Species abundance distributions, statistical mechanics and the priors of maxent. Theor. Popul. Biol.
**2014**, 92, 69–77. [Google Scholar] [CrossRef] [PubMed] - Volkov, I.; Banavar, J.R.; Hubbell, S.P.; Maritan, A. Neutral theory and relative species abundance in ecology. Nature
**2003**, 424, 1035–1037. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Pueyo, S.; He, F.; Zillio, T. The maximum entropy formalism and the idiosyncratic theory of biodiversity. Ecol. Lett.
**2007**, 10, 1017–1028. [Google Scholar] [CrossRef] [PubMed] [Green Version]

**Figure 1.**Illustration of the exponential distribution of the number of naturalized species as a function of the number of sites at which they are found. One species is found at 13 sites. This figure is taken from [1].

© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bowler, M.G.
Ensembles of Atoms, Ensembles of Species: Comparative Statistical Mechanics. *Entropy* **2020**, *22*, 610.
https://doi.org/10.3390/e22060610

**AMA Style**

Bowler MG.
Ensembles of Atoms, Ensembles of Species: Comparative Statistical Mechanics. *Entropy*. 2020; 22(6):610.
https://doi.org/10.3390/e22060610

**Chicago/Turabian Style**

Bowler, Michael G.
2020. "Ensembles of Atoms, Ensembles of Species: Comparative Statistical Mechanics" *Entropy* 22, no. 6: 610.
https://doi.org/10.3390/e22060610