This study provides a brief overview of low energy supersymmetry (SUSY) in light of current experimental constraints, such as collider searches, dark matter searches, and muon g−2 measurements. In addition, we survey a variety of low energy supersymmetric models: the phenomenological minimal supersymmetric model (MSSM); the supersymmetric models with cut-off-scale boundary conditions, i.e., the minimal supergravity (mSUGRA) or the constrained MSSM (CMSSM), the gauge mediation of SUSY breaking (GMSB), and the anomaly mediation of SUSY breaking (AMSB), as well as their extensions. The conclusion is that the low energy SUSY can survive all current experimental constraints and remains compelling, albeit suffering from a slight fine-tuning problem. The advanced models such as mSUGRA, GMSB, and AMSB need to be extended if the muon g−2 anomaly comes from new physics.

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Motivated by the asynchronous finite differences method utilized for the calculation of the most probable distributions of finite particle number systems, this study employs numerical variation and central difference techniques to provide more precise estimations regarding these distributions. Specifically, three novel finite distributions are derived and applied to Bose–Einstein condensation, revealing that the critical condition (nλ3 = 2.612) may be relaxed in finite particle number scenarios. Moreover, maintaining density as a constant is anticipated to result in a higher critical temperature compared to infinite number systems. Notably, the obtained condensate number on the zero-energy level surpasses that of predictions generated by canonical distributions.