## 1 Introduction
However, the analogy can be considered still valid because the 2D skyrmion diameters distribution can be written in a form proportional to a Gaussian distribution in turn depending on the skyrmion energy and, as a result, the configurational entropy can be expressed as a quantity proportional to \(<\)ln\(f_{0}\)\(>\). The aim of this paper is to determine, by means of a simple analytical model, the statistical and statistical thermodynamic properties of a 2D Neel skyrmion diameters distribution. The statistical properties are related to the calculation of the 2D skyrmion diameters distributions, of the most probable and average diameters and of standard deviations of the 2D distributions as a function of temperature \(T\). The average diameters and standard deviations, obtained within the 2D model, are compared with the ones determined within the 3D model. Regarding the statistical thermodynamic properties, the analysis focuses on the calculation of the configurational entropy as a function of the temperature \(T\) and of the external bias field in a 2D framework. This is accomplished investigating the static behavior of a skyrmions population hosted in a ferromagnetic material (e.g., Co) that has the shape of an ultrathin cylindrical dot starting from the skyrmion energy evaluated as a function of the skyrmion diameter in the region of skyrmion metastability [15]. The configurational entropy, calculated according to the 2D model, is then compared with the one obtained via the 3D model and the quantitative differences are discussed. Additionally, as in the 3D model, it is crucial, for characterizing in a quantitative way the 2D distribution, the knowledge of the average diameter, a key quantity appearing in the configurational entropy. It is found that the properties related to the size of skyrmions and the statistical distribution of skyrmion diameters do not essentially depend on the dimensionality of the problem (either 2D or 3D) and the results are very similar in the region of skyrmion metastability. On the other hand, while qualitatively the behavior of the configurational entropy as a function of the temperature is similar, the configurational entropy computed within the 2D approach is considerably smaller than that calculated within the 3D approach. This discrepancy is attributed to the different dependence on the temperature \(T\) of the configurational entropy passing from the 2D to the 3D description and to the role of the thickness of the magnetic skyrmions appearing in the 3D configurational entropy. Moreover, it is found that, within the 2D model, the configurational entropy does not exhibit anymore a decreasing monotonic behavior as a function of the external bias field. According to these results, even though skyrmions are planar structures, the 3D description of a skyrmions population is preferable. It is also given a qualitative description of an entropy data communication system that could be used for a possible future application of the present thermodynamic analysis suggesting the use of skyrmions as temperature and field dependent information entropy carriers. This is based on the complete identification between the configurational entropy at thermodynamic equilibrium calculated here and [PERSON] continuous version of discrete Shannon's information entropy [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. In this respect, very recently, the configurational entropy in 2D skyrmion-like and vortex-like configurations has been investigated for different forms of topological charge density [27] and as a measure of ordering in field configuration space for nonlinear models with spatially-localized energy solutions [28]. Finally, note also that, in the recent literature, there are several papers dealing with the employment of magnetic skyrmions as information carriers but according to completely different approaches based on the skyrmion state and not on the skyrmion entropy (see e.g., [29; 30; 31; 32]). The paper is organized as follows.