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

Edward Bormashenko

doi:10.3390/e24020299

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 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 , where r is the distance between the edge of the string and the current I, and is the Boltzmann constant; ( is adopted). The entropic magnetic force is the repulsion force. The entropic magnetic force scales as , 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.

Highlights

-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]
We demonstrate the temperature dependent magnetic entropic forces emerging when a string of elementary magnets is exerted to the Entropy 2022, 24, 299 demonstrate the temperature dependent magnetic entropic forces emerging when a string magnetic field, which tends to order the magnetsfield, and which in turntends to diminish of of elementary magnets is exerted to the magnetic to orderthe theentropy magnets the system
The general expression for the Helmholtz free energy Φ of a magnetic material exposed The general expression for the Helmholtz free energy Φ of a magnetic material exto the external magnetic field is supplied by Equation (1): posed to the external magnetic field is supplied by Equation (1): 11 → →

Summary

Introduction

-called entropic forces has attracted the attention of investigators in last few decades. 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]. An entropic elastic force that tends to collapse the chain is exerted by the ideal chain between its two free ends [3,4]. 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].

Thermodynamics of Magnetics

Entropic Magnetic Forces in the Field Produced by the Magnetic Dipole

Conclusions