Please use this identifier to cite or link to this item: https://hdl.handle.net/20.500.14365/5042
Title: Statistical mechanical characterization of billiard systems
Authors: Cetin, K.
Tırnaklı, Uğur
Oliveira, D.F.M.
Leonel, E.D.
Keywords: Billiard systems
Nonextensive statistical mechanics
Nonlinear dynamics
Phase space methods
Statistical mechanics
System stability
Area-preserving maps
Billiard systems
Diverse fields
Mechanical characterizations
Model complexes
Nonextensive statistical mechanics
Phase spaces
Probability: distributions
Stability islands
Stable orbit
Probability distributions
Publisher: Elsevier Ltd
Abstract: Area-preserving maps play an important role in diverse fields as they are widely used for modeling complex systems. In addition, these maps provide rich observations by presenting stable orbits and chaotic behavior separately or together in the phase space depending on the control parameter. In recent years, several studies on these maps, drawing inspiration from the phase space dynamics, have shown that nonextensive statistical mechanics provides appropriate instruments to characterize these systems. In this study, we perform a rigorous numerical analysis to delve into the statistical mechanical properties of a billiard system. Our primary goal is to confirm the presence of a q-Gaussian distribution, with an estimated q value of approximately 1.935. We accomplish this by examining the probability distribution of the cumulative sum of system iterates, focusing specifically on initial conditions within the stability islands. Our findings align seamlessly with the latest research in this field. Furthermore, we show that a multi-component probability distribution containing both Gaussian and q-Gaussians describes the entire system for some parameter regions where the phase space consists of stability islands together with the chaotic sea. © 2023 Elsevier Ltd
URI: https://doi.org/10.1016/j.chaos.2023.114331
https://hdl.handle.net/20.500.14365/5042
ISSN: 0960-0779
Appears in Collections:Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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