Abstract
Distribution functions are used for the description of energy distribution of elementary particles, atoms, and molecules in dynamic systems. These distribution functions depend on the energy of the system and on its properties. The paper focuses on the generalization of the relationships commonly used to study the statistical properties of particles in 3D space so that they become generally applicable onto an E-dimensional space. These relationships can then be applied e.g. for studying the properties of the particles in 2D and in 1D space.
Two approaches are discussed to describe the classic (Maxwell Boltzmann) and quantum (Fermi-Dirac, Einstein-Bose) distribution functions. The first approach is based on standard theory of probability, the second one on the fractal theory. We have shown that both approaches lead to the same results for defined boundary conditions. But the validity of the second one, i.e. the fractal approach, is much more general.
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Zmeskal, O., Nespurek, S., Vesely, M., Dzik, P. (2014). Statistics of Fractal Systems. In: Zelinka, I., Suganthan, P., Chen, G., Snasel, V., Abraham, A., Rössler, O. (eds) Nostradamus 2014: Prediction, Modeling and Analysis of Complex Systems. Advances in Intelligent Systems and Computing, vol 289. Springer, Cham. https://doi.org/10.1007/978-3-319-07401-6_6
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DOI: https://doi.org/10.1007/978-3-319-07401-6_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07400-9
Online ISBN: 978-3-319-07401-6
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