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

oleh: Edward Bormashenko

Format: Article
Diterbitkan: MDPI AG 2020-02-01

Deskripsi

The second part of this paper develops an approach suggested in <i>Entropy</i> <b>2020</b>, <i>22</i>(1), 11; which relates ordering in physical systems to symmetrizing. Entropy is frequently interpreted as a quantitative measure of &#8220;chaos&#8221; or &#8220;disorder&#8221;. However, the notions of &#8220;chaos&#8221; and &#8220;disorder&#8221; 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 &#8220;ordering&#8221; 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 <inline-formula> <math display="inline"> <semantics> <mover accent="true"> <mi>H</mi> <mo>&#8594;</mo> </mover> </semantics> </math> </inline-formula>. Imposing symmetry restrictions diminishes the entropy of the system and decreases its temperature. The general case of the system of elementary magnets demonstrating <i>j</i>-fold symmetry is studied. The <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>T</mi> <mi>j</mi> </msub> <mo>=</mo> <mfrac> <mi>T</mi> <mi>j</mi> </mfrac> </mrow> </semantics> </math> </inline-formula> interrelation takes place, where <i>T</i> and <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>T</mi> <mi>j</mi> </msub> </mrow> </semantics> </math> </inline-formula> are the temperatures of non-symmetrized and <i>j</i>-fold-symmetrized systems of the magnets, correspondingly.