# Entropy, Information, and Symmetry; Ordered Is Symmetrical, II: System of Spins in the Magnetic Field

## Abstract

**:**

**2020**, 22(1), 11; which relates ordering in physical systems to symmetrizing. Entropy is frequently interpreted as a quantitative measure of “chaos” or “disorder”. However, the notions of “chaos” and “disorder” are vague and subjective, to a great extent. This leads to numerous misinterpretations of entropy. We propose that the disorder is viewed as an absence of symmetry and identify “ordering” with symmetrizing of a physical system; in other words, introducing the elements of symmetry into an initially disordered physical system. We explore the initially disordered system of elementary magnets exerted to the external magnetic field $\overrightarrow{H}$. Imposing symmetry restrictions diminishes the entropy of the system and decreases its temperature. The general case of the system of elementary magnets demonstrating j-fold symmetry is studied. The ${T}_{j}=\frac{T}{j}$ interrelation takes place, where T and ${T}_{j}$ are the temperatures of non-symmetrized and j-fold-symmetrized systems of the magnets, correspondingly.

## 1. Introduction

## 2. Symmetry and Entropy of Binary Magnetic Systems Embedded into a Magnetic Field

#### 2.1. Symmetrizing and Entropy of 1D Systems Exposed to Magnetic Field $\overrightarrow{H}$

_{2}systems of magnets, Equations. (4c) and 6 yield [12,13,14]:

#### 2.2. Symmetrizing and Entropy of 2D Systems Possessing Axes of Symmetry of Various Orders (j-Fold Symmetry)

## 3. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**A**) The binary 1D system of N non-interacting elementary magnets is shown, exposed to external magnetic field $\overrightarrow{H}\ne 0$. The spin excess of the system is given by $2m=\frac{1}{2}N+m-\left(\frac{1}{2}N-m\right).$ (

**B**) The axis of symmetry shown with a dashed line “arranges” elementary magnets and restricts the number of available configurations of magnets.

**Figure 2.**Schematic representation of a system of elementary magnets possessing axis of symmetry to the order of six, embedded into magnetic field $\overrightarrow{H}$. Magnetic moments and magnetic field $\overrightarrow{H}\text{}$ are normal to the image plane. Maintaining 6-fold symmetry requires simultaneous re-orientation of six magnets (for example, re-orientation of the magnets, marked in Figure 2 with blue color).

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**MDPI and ACS Style**

Bormashenko, E. Entropy, Information, and Symmetry; Ordered Is Symmetrical, II: System of Spins in the Magnetic Field. *Entropy* **2020**, *22*, 235.
https://doi.org/10.3390/e22020235

**AMA Style**

Bormashenko E. Entropy, Information, and Symmetry; Ordered Is Symmetrical, II: System of Spins in the Magnetic Field. *Entropy*. 2020; 22(2):235.
https://doi.org/10.3390/e22020235

**Chicago/Turabian Style**

Bormashenko, Edward. 2020. "Entropy, Information, and Symmetry; Ordered Is Symmetrical, II: System of Spins in the Magnetic Field" *Entropy* 22, no. 2: 235.
https://doi.org/10.3390/e22020235