User talk:GRIPFAST365

October 2021
Hello, and welcome to Wikipedia. This is a message letting you know that one or more of your recent edits to Dark matter have been undone by an automated computer program called ClueBot NG.

Thank you. ClueBot NG (talk) 16:12, 22 October 2021 (UTC)
 * ClueBot NG makes very few mistakes, but it does happen. If you believe the change you made was constructive, please read about it, [ report it here], remove this message from your talk page, and then make the edit again.
 * For help, take a look at the introduction.
 * The following is the log entry regarding this message: Dark matter was changed by GRIPFAST365 (u) (t) ANN scored at 0.979279 on 2021-10-22T16:12:07+00:00

Wikipedia and copyright
Hello GRIPFAST365! Your additions to Dark matter have been removed in whole or in part, as they appear to have added copyrighted content without evidence that the source material is in the public domain or has been released by its owner or legal agent under a suitably-free and compatible copyright license. (To request such a release, see Requesting copyright permission.) While we appreciate your contributions to Wikipedia, there are certain things you must keep in mind about using information from sources to avoid copyright and plagiarism issues.


 * You can only copy/translate a small amount of a source, and you must mark what you take as a direct quotation with double quotation marks (") and cite the source using an inline citation. You can read about this at Non-free content in the sections on "text". See also Help:Referencing for beginners, for how to cite sources here.
 * Aside from limited quotation, you must put all information in your own words and structure, in proper paraphrase. Following the source's words too closely can create copyright problems, so it is not permitted here; see Close paraphrasing. Even when using your own words, you are still, however, asked to cite your sources to verify the information and to demonstrate that the content is not original research.
 * We have strict guidelines on the usage of copyrighted images. Fair use images must meet all ten of the non-free content criteria in order to be used in articles, or they will be deleted. To be used on Wikipedia, all other images must be made available under a free and open copyright license that allows commercial and derivative reuse.
 * If you own the copyright to the source you want to copy or are a legally designated agent, you may be able to license that text so that we can publish it here. Understand, though, that unlike many other sites, where a person can license their content for use there and retain non-free ownership, that is not possible at Wikipedia. Rather, the release of content must be irrevocable, to the world, into either the public domain (PD) or under a suitably-free and compatible copyright license. Such a release must be done in a verifiable manner, so that the authority of the person purporting to release the copyright is evidenced. See Donating copyrighted materials.
 * Also note that Wikipedia articles may not be copied or translated without attribution. If you want to copy or translate from another Wikipedia project or article, you must follow the copyright attribution steps described at Copying within Wikipedia. See also Help:Translation.

It's very important that contributors understand and follow these practices, as policy requires that people who persistently do not must be blocked from editing. If you have any questions about this, you are welcome to leave me a message on my talk page. Thank you. Girth Summit  (blether) 16:21, 22 October 2021 (UTC)


 * Hello, I saw you added this again, so I removed it- please don't copy and paste content in like that. Thank you, Moneytrees🏝️Talk/CCI guide 16:37, 22 October 2021 (UTC)
 * Wow - so, after I went to the trouble of removing that edit, and explaining to you why I did so, you just reinstate it? You're a new user, and we try to be nice to new users, but please understand that you are wasting other people's time when you make edits like that - you must not copy and paste from websites. If you reinstate that again, your account will be blocked from editing. Best Girth Summit  (blether)  16:44, 22 October 2021 (UTC)

You wanna stop lying and name all those stars after lucas leslie

I made bitcoin bnb ethereum busd doge

ethereum classic

tron

shiba inu Avalanche Cardano Bitcoin bep2 Xrp Litecoin Tether Zcash

I need you to make a page for lucas james ross leslie for all the cryptocurrencies please

Check the bitcoin live node map

I am Satoshi Nakamoto GRIPFAST365 (talk) 13:19, 22 September 2022 (UTC)

Binance ftx coinbase GRIPFAST365 (talk) 13:20, 22 September 2022 (UTC)

December 2021
Hello, and welcome to Wikipedia. This is a message letting you know that one or more of your recent edits to Ross 128 b have been undone by an automated computer program called ClueBot NG.

Thank you. ClueBot NG (talk) 21:18, 11 December 2021 (UTC)
 * ClueBot NG makes very few mistakes, but it does happen. If you believe the change you made was constructive, please read about it, [ report it here], remove this message from your talk page, and then make the edit again.
 * For help, take a look at the introduction.
 * The following is the log entry regarding this message: Ross 128 b was changed by GRIPFAST365 (u) (t) ANN scored at 0.867248 on 2021-12-11T21:18:00+00:00

Please stop your disruptive editing. If you continue to vandalize Wikipedia, you may be blocked from editing. Knuthove (talk) 22:30, 11 December 2021 (UTC)

You may be blocked from editing without further warning the next time you vandalize Wikipedia, as you did at Gliese 832 c. Knuthove (talk) 22:31, 11 December 2021 (UTC)

 You have been blocked indefinitely from editing because your account is being used only for vandalism. If you think there are good reasons for being unblocked, please read the guide to appealing blocks, then add the following text below the block notice on your talk page:. Bbb23 (talk) 22:55, 11 December 2021 (UTC)

GRAVITY
An emergent phenomenon is an extension of this self-organization phenomenon. However, there are some differences between them. Self-organization is the one-way formation of macroscopic order from micro dynamics, whereas emergent phenomenon is the circulation of recurrent information from macro to micro, and vice versa.Nov 13, 2017 GRIPFAST365 (talk) 15:18, 22 September 2022 (UTC)

Which scientist proposed the gravity could be an emergent phenomenon?

Historically, the idea the gravity could be an emergent phenomenon was first emphasised by Sakharov in the sixties, and one specific implementation of this paradigm was suggested by Ted Jacobson in 1995.

GRIPFAST365 (talk) 15:19, 22 September 2022 (UTC)

Gravity changes things. Expansion of a self-gravitating gas (definitionally) increases the gas's volume (which increases the entropy), but it also increases the potential energy and thus decreases the kinetic energy, as particles must do work against the attractive gravitational field. GRIPFAST365 (talk) 15:19, 22 September 2022 (UTC)

zoom_out_map search menu

Journals

Entropy

Volume 24

Issue 2

10.3390/e24020299

settings

Open AccessArticle

Magnetic Entropic Forces Emerging in the System of Elementary Magnets Exposed to the Magnetic Field

by

Edward Bormashenko

Chemical Engineering Department, Engineering Sciences Faculty, Ariel University, Ariel 407000, Israel

Academic Editor: Dimitri Volchenkov

Entropy 2022, 24(2), 299; https://doi.org/10.3390/e24020299

Received: 3 February 2022 / Revised: 17 February 2022 / Accepted: 18 February 2022 / Published: 20 February 2022

(This article belongs to the Special Issue Entropic Forces in Complex Systems II)

Download PDF

Browse Figures

Figure 1

The linear system (string) of elementary magnets shown with arrows exerted to the permanent magnetic field generated by the infinite direct current I is depicted. Current I is perpendicular to the plane of the drawing. The length of the string is L; the distance between the current and the edge of the string is r.

" style="box-sizing: border-box; color: rgb(79, 86, 113); line-height: inherit; text-decoration: none; max-height: 1e+06px; font-weight: 700;">Figure 2

Direct current I embedded into the medium built of magnetic moments μ→. The magnetic entropic force given by Equation (9) will repulse the magnetic moments, thus giving rise to the “entropic pressure phenomenon”.

" style="box-sizing: border-box; color: rgb(79, 86, 113); line-height: inherit; text-decoration: none; max-height: 1e+06px; font-weight: 700;">Figure 3

The linear system (string) of elementary magnets shown with arrows exerted to the permanent magnetic field generated by the magnetic dipole M→ I is depicted. The length of the string is L; the distance between the center of the magnetic dipole and the edge of the string is r.

" style="box-sizing: border-box; color: rgb(79, 86, 113); line-height: inherit; text-decoration: none; max-height: 1e+06px; font-weight: 700;">

Review Reports Citation Export

Abstract

A temperature dependent entropic force acting between the straight direct current I and the linear system (string with length of L) of N elementary non-interacting magnets/spins &#x3BC;&#x2192;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">μ⃗  is reported. The system of elementary magnets is supposed to be in the thermal equilibrium with the infinite thermal bath T. The entropic force at large distance from the current scales as Fmagnen~1r3" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Fenmagn~1r3, where r is the distance between the edge of the string and the current I, and kB" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">kB is the Boltzmann constant; (r&#x226B;L" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">r≫L is adopted). The entropic magnetic force is the repulsion force. The entropic magnetic force scales as Fmagnen~1T" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Fenmagn~1T, which is unusual for entropic forces. The effect of “entropic pressure” is predicted for the situation when the source of the magnetic field is embedded into the continuous media, comprising elementary magnets/spins. Interrelation between bulk and entropy magnetic forces is analyzed. Entropy forces acting on the 1D string of elementary magnets that exposed the magnetic field produced by the magnetic dipole are addressed.

Keywords: entropic force; magnetic field; linear system of elementary magnets; ordering; temperature; repulsion force

1. Introduction

So-called entropic forces has attracted the attention of investigators in last few decades. An entropic force acting in a system is an emergent phenomenon resulting from the entire system’s statistical tendency to increase its entropy [1,2]. Entropic force represents the tendency of a system to evolve into a more probable state, rather than simply into one of lower potential energy [1,2]. A classic example of an entropic force is the temperature dependent elasticity of a freely-jointed polymer chain [3,4]. For an ideal polymer chain, maximizing its entropy means reducing the distance between its two free ends [3,4]. Consequently, an entropic elastic force that tends to collapse the chain is exerted by the ideal chain between its two free ends [3,4]. Muscles of mammals are also driven by entropy forces [5]. As it has been shown, elasticity in the giant muscle protein titin arises from entropy in a way very similar to the entropy-driven elasticity of polymer chains [5]. The so-called “hydrophobic effect” represents additional exemplification of the entropy-forces-driven phenomena. The hydrophobic interaction originates from the disruption of hydrogen bonds between molecules of liquid water by the nonpolar solute [6]. By aggregating together, nonpolar molecules reduce the surface area exposed to water and minimize the effect [6]. This reducing of the surface is thermodinamically (entropically) favorable, giving rise to the clustering of small hydrophobic particles [6]. An interest to entropic force was strengthened after the suggestion of Verlinde, who hypothesized the entropic nature of gravity [7]. The entropic origin of gravity was discussed in detail in Refs. [8,9]. It was shown that classical Newtonian gravity may be interpreted in terms of an entropic force [8,9]. The entropy origin of gravity was criticized in Refs. [10,11,12], and the problem remains open and debatable. Motivated by Verlinde’s theory of entropic gravity, a tentative explanation to the Coulomb’s law with an entropic force was suggested [13]. We demonstrate the temperature dependent magnetic entropic forces emerging when a string of elementary magnets is exerted to the magnetic field, which tends to order the magnets and in turn to diminish the entropy of the system.

2. Results and Discussion2.1. Thermodynamics of Magnetics: Origin of Entropy Forces

The general expression for the Helmholtz free energy &#x3A6;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Φ of a magnetic material exposed to the external magnetic field is supplied by Equation (1):

d&#x3A6;=&#x2212;SdT&#x2212;TdS+&#x3B6;dN+12H&#x2192;&#xB7;B&#x2192;dV&#xA0;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 12.87px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">dΦ=−SdT−TdS+ζdN+12H→⋅B→dV

(1)

where S, T, and V are the entropy, temperature, and volume of the magnetic body correspondingly, H&#x2192;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">H→ and B&#x2192;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">B→ are the magnetic field and magnetic flux intensities, and &#x3B6;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">

GRIPFAST365 (talk) 15:32, 22 September 2022 (UTC)

Figure 1. The linear system (string) of elementary magnets shown with arrows exerted to the permanent magnetic field generated by the infinite direct current I is depicted. Current I is perpendicular to the plane of the drawing. The length of the string is L; the distance between the current and the edge of the string is r.

We assume that there are N separate and distinct sites fixed in a space and aligned, as shown in Figure 1. Attached to each site is an elementary magnet, which can point only up or down, as shown in Figure 1. The total length of the string is L, and the linear density of the magnets N&#x2DC;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">N˜, defined according to Equation (3), is supposed to be constant along the string:

N&#x2DC;=NL=const" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 12.87px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">N˜=NL=const

(3)

The suggested 1D string built of elementary magnets/spins &#x3BC;&#x2192;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">μ⃗  is embedded into magnetic field H&#x2192;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">H→ generated by the infinite straight current H(r)=I2&#x3C0;r" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">H(r)=I2πr, as shown in Figure 1, leading to the spin orientation. The potential energy of a single elementary magnet in the magnetic field is given in the SI system of units by Equation (4):

U(r)=&#x2212;&#x3BC;0&#x3BC;&#x2192;&#xB7;H&#x2192;(r)" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 12.87px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">U(r)=−μ0μ⃗ ⋅H→(r)

(4)

where &#x3BC;0" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">μ0 is the vacuum permeability. Assume also that the system of spins is in the thermal equilibrium with the surrounding (thermal bath) under the constant temperature T (the system is isothermal). Let us divide the string of the magnets into “sub-strings” as follows: let dNi" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">dNi be the number of spins in the sub-string dri" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">dri numbered “i”, the magnetic field within the string is H(ri)=I2&#x3C0;ri" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">H(ri)=I2πri (distance ri" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">ri is shown in Figure 1). The entropy of the sub-string Si" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Si was addressed in detail in [16,17], and within the approximation of the weak magnetic field, i.e., when &#x3BC;0&#x3BC;H&#x226A;kBT" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">μ0μH≪kBT takes place (kB" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">

GRIPFAST365 (talk) 15:34, 22 September 2022 (UTC)

zoom_out_map search menu

Journals

Entropy

Volume 24

Issue 2

10.3390/e24020299

settings

Open AccessArticle

Magnetic Entropic Forces Emerging in the System of Elementary Magnets Exposed to the Magnetic Field

by

Edward Bormashenko

Chemical Engineering Department, Engineering Sciences Faculty, Ariel University, Ariel 407000, Israel

Academic Editor: Dimitri Volchenkov

Entropy 2022, 24(2), 299; https://doi.org/10.3390/e24020299

Received: 3 February 2022 / Revised: 17 February 2022 / Accepted: 18 February 2022 / Published: 20 February 2022

(This article belongs to the Special Issue Entropic Forces in Complex Systems II)

Download PDF

Browse Figures

Figure 1

The linear system (string) of elementary magnets shown with arrows exerted to the permanent magnetic field generated by the infinite direct current I is depicted. Current I is perpendicular to the plane of the drawing. The length of the string is L; the distance between the current and the edge of the string is r.

" style="box-sizing: border-box; color: rgb(79, 86, 113); line-height: inherit; text-decoration: none; max-height: 1e+06px; font-weight: 700;">Figure 2

Direct current I embedded into the medium built of magnetic moments μ→. The magnetic entropic force given by Equation (9) will repulse the magnetic moments, thus giving rise to the “entropic pressure phenomenon”.

" style="box-sizing: border-box; color: rgb(79, 86, 113); line-height: inherit; text-decoration: none; max-height: 1e+06px; font-weight: 700;">Figure 3

The linear system (string) of elementary magnets shown with arrows exerted to the permanent magnetic field generated by the magnetic dipole M→ I is depicted. The length of the string is L; the distance between the center of the magnetic dipole and the edge of the string is r.

" style="box-sizing: border-box; color: rgb(79, 86, 113); line-height: inherit; text-decoration: none; max-height: 1e+06px; font-weight: 700;">

Review Reports Citation Export

Abstract

A temperature dependent entropic force acting between the straight direct current I and the linear system (string with length of L) of N elementary non-interacting magnets/spins &#x3BC;&#x2192;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">μ⃗  is reported. The system of elementary magnets is supposed to be in the thermal equilibrium with the infinite thermal bath T. The entropic force at large distance from the current scales as Fmagnen~1r3" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Fenmagn~1r3, where r is the distance between the edge of the string and the current I, and kB" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">kB is the Boltzmann constant; (r&#x226B;L" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">r≫L is adopted). The entropic magnetic force is the repulsion force. The entropic magnetic force scales as Fmagnen~1T" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Fenmagn~1T, which is unusual for entropic forces. The effect of “entropic pressure” is predicted for the situation when the source of the magnetic field is embedded into the continuous media, comprising elementary magnets/spins. Interrelation between bulk and entropy magnetic forces is analyzed. Entropy forces acting on the 1D string of elementary magnets that exposed the magnetic field produced by the magnetic dipole are addressed.

Keywords: entropic force; magnetic field; linear system of elementary magnets; ordering; temperature; repulsion force

1. Introduction

So-called entropic forces has attracted the attention of investigators in last few decades. An entropic force acting in a system is an emergent phenomenon resulting from the entire system’s statistical tendency to increase its entropy [1,2]. Entropic force represents the tendency of a system to evolve into a more probable state, rather than simply into one of lower potential energy [1,2]. A classic example of an entropic force is the temperature dependent elasticity of a freely-jointed polymer chain [3,4]. For an ideal polymer chain, maximizing its entropy means reducing the distance between its two free ends [3,4]. Consequently, an entropic elastic force that tends to collapse the chain is exerted by the ideal chain between its two free ends [3,4]. Muscles of mammals are also driven by entropy forces [5]. As it has been shown, elasticity in the giant muscle protein titin arises from entropy in a way very similar to the entropy-driven elasticity of polymer chains [5]. The so-called “hydrophobic effect” represents additional exemplification of the entropy-forces-driven phenomena. The hydrophobic interaction originates from the disruption of hydrogen bonds between molecules of liquid water by the nonpolar solute [6]. By aggregating together, nonpolar molecules reduce the surface area exposed to water and minimize the effect [6]. This reducing of the surface is thermodinamically (entropically) favorable, giving rise to the clustering of small hydrophobic particles [6]. An interest to entropic force was strengthened after the suggestion of Verlinde, who hypothesized the entropic nature of gravity [7]. The entropic origin of gravity was discussed in detail in Refs. [8,9]. It was shown that classical Newtonian gravity may be interpreted in terms of an entropic force [8,9]. The entropy origin of gravity was criticized in Refs. [10,11,12], and the problem remains open and debatable. Motivated by Verlinde’s theory of entropic gravity, a tentative explanation to the Coulomb’s law with an entropic force was suggested [13]. We demonstrate the temperature dependent magnetic entropic forces emerging when a string of elementary magnets is exerted to the magnetic field, which tends to order the magnets and in turn to diminish the entropy of the system.

2. Results and Discussion2.1. Thermodynamics of Magnetics: Origin of Entropy Forces

The general expression for the Helmholtz free energy &#x3A6;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Φ of a magnetic material exposed to the external magnetic field is supplied by Equation (1):

d&#x3A6;=&#x2212;SdT&#x2212;TdS+&#x3B6;dN+12H&#x2192;&#xB7;B&#x2192;dV&#xA0;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 12.87px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">dΦ=−SdT−TdS+ζdN+12H→⋅B→dV

(1)

where S, T, and V are the entropy, temperature, and volume of the magnetic body correspondingly, H&#x2192;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">H→ and B&#x2192;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">B→ are the magnetic field and magnetic flux intensities, and &#x3B6;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">

GRIPFAST365 (talk) 15:35, 22 September 2022 (UTC)

zoom_out_map search menu

Journals

Entropy

Volume 24

Issue 2

10.3390/e24020299

settings

Open AccessArticle

Magnetic Entropic Forces Emerging in the System of Elementary Magnets Exposed to the Magnetic Field

by

Edward Bormashenko

Chemical Engineering Department, Engineering Sciences Faculty, Ariel University, Ariel 407000, Israel

Academic Editor: Dimitri Volchenkov

Entropy 2022, 24(2), 299; https://doi.org/10.3390/e24020299

Received: 3 February 2022 / Revised: 17 February 2022 / Accepted: 18 February 2022 / Published: 20 February 2022

(This article belongs to the Special Issue Entropic Forces in Complex Systems II)

Download PDF

Browse Figures

Figure 1

The linear system (string) of elementary magnets shown with arrows exerted to the permanent magnetic field generated by the infinite direct current I is depicted. Current I is perpendicular to the plane of the drawing. The length of the string is L; the distance between the current and the edge of the string is r.

" style="box-sizing: border-box; color: rgb(79, 86, 113); line-height: inherit; text-decoration: none; max-height: 1e+06px; font-weight: 700;">Figure 2

Direct current I embedded into the medium built of magnetic moments μ→. The magnetic entropic force given by Equation (9) will repulse the magnetic moments, thus giving rise to the “entropic pressure phenomenon”.

" style="box-sizing: border-box; color: rgb(79, 86, 113); line-height: inherit; text-decoration: none; max-height: 1e+06px; font-weight: 700;">Figure 3

The linear system (string) of elementary magnets shown with arrows exerted to the permanent magnetic field generated by the magnetic dipole M→ I is depicted. The length of the string is L; the distance between the center of the magnetic dipole and the edge of the string is r.

" style="box-sizing: border-box; color: rgb(79, 86, 113); line-height: inherit; text-decoration: none; max-height: 1e+06px; font-weight: 700;">

Review Reports Citation Export

Abstract

A temperature dependent entropic force acting between the straight direct current I and the linear system (string with length of L) of N elementary non-interacting magnets/spins &#x3BC;&#x2192;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">μ⃗  is reported. The system of elementary magnets is supposed to be in the thermal equilibrium with the infinite thermal bath T. The entropic force at large distance from the current scales as Fmagnen~1r3" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Fenmagn~1r3, where r is the distance between the edge of the string and the current I, and kB" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">kB is the Boltzmann constant; (r&#x226B;L" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">r≫L is adopted). The entropic magnetic force is the repulsion force. The entropic magnetic force scales as Fmagnen~1T" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Fenmagn~1T, which is unusual for entropic forces. The effect of “entropic pressure” is predicted for the situation when the source of the magnetic field is embedded into the continuous media, comprising elementary magnets/spins. Interrelation between bulk and entropy magnetic forces is analyzed. Entropy forces acting on the 1D string of elementary magnets that exposed the magnetic field produced by the magnetic dipole are addressed.

Keywords: entropic force; magnetic field; linear system of elementary magnets; ordering; temperature; repulsion force

1. Introduction

So-called entropic forces has attracted the attention of investigators in last few decades. An entropic force acting in a system is an emergent phenomenon resulting from the entire system’s statistical tendency to increase its entropy [1,2]. Entropic force represents the tendency of a system to evolve into a more probable state, rather than simply into one of lower potential energy [1,2]. A classic example of an entropic force is the temperature dependent elasticity of a freely-jointed polymer chain [3,4]. For an ideal polymer chain, maximizing its entropy means reducing the distance between its two free ends [3,4]. Consequently, an entropic elastic force that tends to collapse the chain is exerted by the ideal chain between its two free ends [3,4]. Muscles of mammals are also driven by entropy forces [5]. As it has been shown, elasticity in the giant muscle protein titin arises from entropy in a way very similar to the entropy-driven elasticity of polymer chains [5]. The so-called “hydrophobic effect” represents additional exemplification of the entropy-forces-driven phenomena. The hydrophobic interaction originates from the disruption of hydrogen bonds between molecules of liquid water by the nonpolar solute [6]. By aggregating together, nonpolar molecules reduce the surface area exposed to water and minimize the effect [6]. This reducing of the surface is thermodinamically (entropically) favorable, giving rise to the clustering of small hydrophobic particles [6]. An interest to entropic force was strengthened after the suggestion of Verlinde, who hypothesized the entropic nature of gravity [7]. The entropic origin of gravity was discussed in detail in Refs. [8,9]. It was shown that classical Newtonian gravity may be interpreted in terms of an entropic force [8,9]. The entropy origin of gravity was criticized in Refs. [10,11,12], and the problem remains open and debatable. Motivated by Verlinde’s theory of entropic gravity, a tentative explanation to the Coulomb’s law with an entropic force was suggested [13]. We demonstrate the temperature dependent magnetic entropic forces emerging when a string of elementary magnets is exerted to the magnetic field, which tends to order the magnets and in turn to diminish the entropy of the system.

2. Results and Discussion2.1. Thermodynamics of Magnetics: Origin of Entropy Forces

The general expression for the Helmholtz free energy &#x3A6;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Φ of a magnetic material exposed to the external magnetic field is supplied by Equation (1):

d&#x3A6;=&#x2212;SdT&#x2212;TdS+&#x3B6;dN+12H&#x2192;&#xB7;B&#x2192;dV&#xA0;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 12.87px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">dΦ=−SdT−TdS+ζdN+12H→⋅B→dV

(1)

where S, T, and V are the entropy, temperature, and volume of the magnetic body correspondingly, H&#x2192;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">H→ and B&#x2192;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">B→ are the magnetic field and magnetic flux intensities, and &#x3B6;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">

GRIPFAST365 (talk) 15:38, 22 September 2022 (UTC)

zoom_out_map search menu

Journals

Entropy

Volume 24

Issue 2

10.3390/e24020299

settings

Open AccessArticle

Magnetic Entropic Forces Emerging in the System of Elementary Magnets Exposed to the Magnetic Field

by

Edward Bormashenko

Chemical Engineering Department, Engineering Sciences Faculty, Ariel University, Ariel 407000, Israel

Academic Editor: Dimitri Volchenkov

Entropy 2022, 24(2), 299; https://doi.org/10.3390/e24020299

Received: 3 February 2022 / Revised: 17 February 2022 / Accepted: 18 February 2022 / Published: 20 February 2022

(This article belongs to the Special Issue Entropic Forces in Complex Systems II)

Download PDF

Browse Figures

Figure 1

The linear system (string) of elementary magnets shown with arrows exerted to the permanent magnetic field generated by the infinite direct current I is depicted. Current I is perpendicular to the plane of the drawing. The length of the string is L; the distance between the current and the edge of the string is r.

" style="box-sizing: border-box; color: rgb(79, 86, 113); line-height: inherit; text-decoration: none; max-height: 1e+06px; font-weight: 700;">Figure 2

Direct current I embedded into the medium built of magnetic moments μ→. The magnetic entropic force given by Equation (9) will repulse the magnetic moments, thus giving rise to the “entropic pressure phenomenon”.

" style="box-sizing: border-box; color: rgb(79, 86, 113); line-height: inherit; text-decoration: none; max-height: 1e+06px; font-weight: 700;">Figure 3

The linear system (string) of elementary magnets shown with arrows exerted to the permanent magnetic field generated by the magnetic dipole M→ I is depicted. The length of the string is L; the distance between the center of the magnetic dipole and the edge of the string is r.

" style="box-sizing: border-box; color: rgb(79, 86, 113); line-height: inherit; text-decoration: none; max-height: 1e+06px; font-weight: 700;">

Review Reports Citation Export

Abstract

A temperature dependent entropic force acting between the straight direct current I and the linear system (string with length of L) of N elementary non-interacting magnets/spins &#x3BC;&#x2192;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">μ⃗  is reported. The system of elementary magnets is supposed to be in the thermal equilibrium with the infinite thermal bath T. The entropic force at large distance from the current scales as Fmagnen~1r3" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Fenmagn~1r3, where r is the distance between the edge of the string and the current I, and kB" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">kB is the Boltzmann constant; (r&#x226B;L" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">r≫L is adopted). The entropic magnetic force is the repulsion force. The entropic magnetic force scales as Fmagnen~1T" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Fenmagn~1T, which is unusual for entropic forces. The effect of “entropic pressure” is predicted for the situation when the source of the magnetic field is embedded into the continuous media, comprising elementary magnets/spins. Interrelation between bulk and entropy magnetic forces is analyzed. Entropy forces acting on the 1D string of elementary magnets that exposed the magnetic field produced by the magnetic dipole are addressed.

Keywords: entropic force; magnetic field; linear system of elementary magnets; ordering; temperature; repulsion force

1. Introduction

So-called entropic forces has attracted the attention of investigators in last few decades. An entropic force acting in a system is an emergent phenomenon resulting from the entire system’s statistical tendency to increase its entropy [1,2]. Entropic force represents the tendency of a system to evolve into a more probable state, rather than simply into one of lower potential energy [1,2]. A classic example of an entropic force is the temperature dependent elasticity of a freely-jointed polymer chain [3,4]. For an ideal polymer chain, maximizing its entropy means reducing the distance between its two free ends [3,4]. Consequently, an entropic elastic force that tends to collapse the chain is exerted by the ideal chain between its two free ends [3,4]. Muscles of mammals are also driven by entropy forces [5]. As it has been shown, elasticity in the giant muscle protein titin arises from entropy in a way very similar to the entropy-driven elasticity of polymer chains [5]. The so-called “hydrophobic effect” represents additional exemplification of the entropy-forces-driven phenomena. The hydrophobic interaction originates from the disruption of hydrogen bonds between molecules of liquid water by the nonpolar solute [6]. By aggregating together, nonpolar molecules reduce the surface area exposed to water and minimize the effect [6]. This reducing of the surface is thermodinamically (entropically) favorable, giving rise to the clustering of small hydrophobic particles [6]. An interest to entropic force was strengthened after the suggestion of Verlinde, who hypothesized the entropic nature of gravity [7]. The entropic origin of gravity was discussed in detail in Refs. [8,9]. It was shown that classical Newtonian gravity may be interpreted in terms of an entropic force [8,9]. The entropy origin of gravity was criticized in Refs. [10,11,12], and the problem remains open and debatable. Motivated by Verlinde’s theory of entropic gravity, a tentative explanation to the Coulomb’s law with an entropic force was suggested [13]. We demonstrate the temperature dependent magnetic entropic forces emerging when a string of elementary magnets is exerted to the magnetic field, which tends to order the magnets and in turn to diminish the entropy of the system.

2. Results and Discussion2.1. Thermodynamics of Magnetics: Origin of Entropy Forces

The general expression for the Helmholtz free energy &#x3A6;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Φ of a magnetic material exposed to the external magnetic field is supplied by Equation (1):

d&#x3A6;=&#x2212;SdT&#x2212;TdS+&#x3B6;dN+12H&#x2192;&#xB7;B&#x2192;dV&#xA0;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 12.87px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">dΦ=−SdT−TdS+ζdN+12H→⋅B→dV

(1)

where S, T, and V are the entropy, temperature, and volume of the magnetic body correspondingly, H&#x2192;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">H→ and B&#x2192;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">B→ are the magnetic field and magnetic flux intensities, and &#x3B6;" role="presentation" style="box-sizing: border-box; max-height: none; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.3px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">

GRIPFAST365 (talk) 15:39, 22 September 2022 (UTC)

https://scholar.google.com/scholar_lookup?title=Entropy,+Information,+and+Symmetry;+Ordered+Is+Symmetrical,+II:+System+of+Spins+in+the+Magnetic+Field&author=Bormashenko,+E.&publication_year=2020&journal=Entropy&volume=22&pages=235&doi=10.3390/e22020235&pmid=33286009 GRIPFAST365 (talk) 15:41, 22 September 2022 (UTC)

systemic passive vacuum definition GRIPFAST365 (talk) 16:38, 22 September 2022 (UTC)

Passive vacuum, also referred to as a 'one-way valve', provides a high level of socket comfort when a vacuum is created between the suspension sleeve and the liner/skin. GRIPFAST365 (talk) 16:39, 22 September 2022 (UTC)

sym·met·ri·cal

/səˈmetrik(ə)l/

adjective

made up of exactly similar parts facing each other or around an axis; showing symmetry.

"the shape of a hill, smooth and symmetrical"

GRIPFAST365 (talk) 16:40, 22 September 2022 (UTC)