# Compositional Closure—Its Origin Lies Not in Mathematics but Rather in Nature Itself

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Components—The Physical Variables Being Measured in a Sample

#### 2.1. Immutable Variables

#### 2.2. Reactive Variables

## 3. Systems—Whether Components Can Enter or Leave

#### 3.1. Closed Systems

#### 3.2. Open Systems

#### 3.2.1. Displacive Open Systems—Crowding

#### 3.2.2. Accommodative Open Systems

^{−1}, mol L

^{−1}, etc. (relative to seawater—mass or volume); or heavy metals in airborne particulate matter as ng m

^{3−}, etc. (relative to air volume).

#### 3.2.3. Partly Accommodative Systems

^{+}(numerator approaching denominator).

## 4. Results

#### 4.1. The Six Combinations of Systems and Components

#### 4.1.1. The Two Closed System Types

#### 4.1.2. The Four Open System Types

## 5. Discussion

#### 5.1. Statistical Closure Implications

#### 5.2. Intermediate Open Systems

#### 5.3. Immutable vs. Reactive Displacive Systems

#### 5.4. The Accommodative–Displacive System Paradox

#### 5.5. Another Example of the Accommodative–Displacive System Paradox

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Compositional closure status in closed systems with immutable and with reactive components and examples thereof.

**Figure 2.**Compositional closure status in accommodative and displacive open systems with immutable and with reactive components and examples thereof.

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**MDPI and ACS Style**

Pingitore, N.E., Jr.; Engle, M.A.
Compositional Closure—Its Origin Lies Not in Mathematics but Rather in Nature Itself. *Minerals* **2022**, *12*, 74.
https://doi.org/10.3390/min12010074

**AMA Style**

Pingitore NE Jr., Engle MA.
Compositional Closure—Its Origin Lies Not in Mathematics but Rather in Nature Itself. *Minerals*. 2022; 12(1):74.
https://doi.org/10.3390/min12010074

**Chicago/Turabian Style**

Pingitore, Nicholas E., Jr., and Mark A. Engle.
2022. "Compositional Closure—Its Origin Lies Not in Mathematics but Rather in Nature Itself" *Minerals* 12, no. 1: 74.
https://doi.org/10.3390/min12010074