# 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

## References

- Mikhailovsky, G.E.; Levich, A.P. Entropy, information and complexity or which aims the arrow of time? Entropy
**2015**, 17, 4863–4890. [Google Scholar] [CrossRef] [Green Version] - Mikhailovsky, G. From Identity to uniqueness: The Emergence of increasingly higher levels of hierarchy in the process of the matter evolution. Entropy
**2018**, 20, 533. [Google Scholar] [CrossRef] [Green Version] - Muñoz-Bonilla, A.; Fernández-García, M.; Rodríguez-Hernández, J. Towards hierarchically ordered functional porous polymeric surfaces prepared by the breath figures approach. Prog. Polym. Sci.
**2014**, 39, 510–554. [Google Scholar] [CrossRef] [Green Version] - Adamatzky, A.; Mayne, R. Actin automata: Phenomenology and localizations. Int. J. Bifurc. Chaos
**2015**, 25, 1550030. [Google Scholar] [CrossRef] [Green Version] - Adamatzky, A. On diversity of configurations generated by excitable cellular automata with dynamical excitation interval. Int. J. Mod. Phys. C
**2012**, 23, 1250085. [Google Scholar] [CrossRef] [Green Version] - Nosonovsky, M. Entropy in tribology: In the search for applications. Entropy
**2010**, 12, 1345–1390. [Google Scholar] [CrossRef] - Falk, G. Entropy, a resurrection of caloric-a look at the history of thermodynamics. Eur. J. Phys.
**1985**, 6, 108–115. [Google Scholar] [CrossRef] [Green Version] - Martin, J.S.; Smith, N.A.; Francis, C.D. Removing the entropy from the definition of entropy: Clarifying the relationship between evolution, entropy, and the second law of thermodynamics. Evol. Educ. Outreach
**2013**, 6, 30. [Google Scholar] [CrossRef] - Gaudenzi, R. Entropy? Exercices de Style. Entropy
**2019**, 21, 742. [Google Scholar] [CrossRef] [Green Version] - Wright, P.G. Entropy and disorder. Contemp. Phys.
**1970**, 11, 581–588. [Google Scholar] [CrossRef] - Bormashenko, E.D. Entropy, information, and symmetry: Ordered is symmetrical. Entropy
**2020**, 22, 11. [Google Scholar] [CrossRef] [Green Version] - Baierlein, R. Thermal Physics; Cambridge University Press: Cambridge, UK, 1999. [Google Scholar]
- Landau, L.D.; Lifshitz, E.M. Statistical Physics, 3rd ed.; Course of Theoretical Physics; Elsevier: Oxford, UK, 2011; Volume 5. [Google Scholar]
- Kittel, C.H. Thermal Physics; John and Wiley & Sons: New York, NY, USA, 1969. [Google Scholar]

**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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## Share and Cite

**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