The study of thermodynamics of topological defects is an important challenge to understand their underlying physics. Among them, magnetic skyrmions have a leading role for their physical properties and potential applications in storage and neuromorphic computing. In this paper, the thermodynamic statistics of magnetic skyrmions is derived. It is shown that the skyrmion free energy can be modelled via a parabolic function and the diameters statistics obeys the Maxwell-Boltzmann distribution. This allows for making an analogy between the behavior of the distribution of skyrmion diameters statistics and the diluted gas Maxwell-Boltzmann molecules distribution at thermodynamical equilibrium. The calculation of the skyrmion configurational entropy, due to thermally-induced changes of size and shape of the skyrmion, is essential for the determination of thermal fluctuations of the skyrmion energy around its average value. These results can be employed to advance the field of skyrmionics.
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I. INTRODUCTIONMagnetic skyrmions have been gaining an important role in studies of low-dimensional magnetic systems due to their suitable physical properties and potential applications [1][2][3][4]. Skyrmions can be considered as quasi-particles with topologically-protected magnetization texture, characterized by an integer skyrmion number [1,4]. Although skyrmions can be stabilized by the interplay between exchange and dipolar interactions (so called "bubble skyrmion" [1]), much of the interest is devoted to systems where the Dzyaloshinskii-Moriya interaction (DMI) plays a role in this stabilization [5,6].The DMI is a chiral exchange interaction due to lack or breaking of inversion symmetry in bulk crystalline lattices (bulk DMI) [7][8][9] or at the interfaces in magnetic multilayers (interfacial DMI (IDMI)) [10-13]. While other types of DMI can exist (for instance, in D2d structures) [14,15], in this work we focus on the IDMI. This because it promotes the formation of small Néel skyrmions [1,2,4], which are stable at room temperature as isolated skyrmions, and can be nucleated [16-18], manipulated [12,19-21] as well as detected [22-24] by electrical currents. Therefore, Néel skyrmions have become promising for technological applications [25-33]. Fundamentally, because of thermal fluctuations, Néel skyrmions are subject to (i) internal deformations [10,12,34,35], that are responsible for the loss of the circular symmetry; (ii) thermal drift [18,34,35], which leads to a random skyrmion motion throughout the film plane; (iii) thermal breathing modes [35,36] that can induce non-stationary expansion and shrinking of the skyrmion core, i.e. a time-evolution of the skyrmion size. Hence, the effect of thermal fluctuations should be considered for a proper design of skyrmionbased devices and applications [32,35], especially at room temperature.In this work, we show that the thermal fluctuations promote the existence of a number of skyrmions characterized by the same energy, but having different shapes and diameters. This aspect allows us f...