AI 中文总结
本研究以谐振子能谱为基础，采用Tsallis与Renyi熵测度，探究非对易参数θ与广义熵指数q间的内在联系，为时空几何与广义统计力学的相互作用提供新见解。
AI 中文摘要
本研究利用谐振子的能谱，通过熵将其动力学行为与统计力学形式体系相连接。我们在对易与非对易二维位形空间中，对该能谱产生的熵进行热分析，采用Tsallis和Renyi熵测度。主要目标是探究非对易参数(θ)与广义熵产生的参数之间是否存在内在联系及相互影响。通过分析Tsallis和Renyi两种框架，我们研究θ与熵指数q之间是否存在基本关系。建立此类联系可为时空几何与广义统计力学之间的相互作用提供新的见解。
英文摘要
In this study, we use the harmonic oscillator s energy spectrum to connect its dynamical behavior to the formalism of statistical mechanics through entropy. We perform a thermal analysis of the entropy generated by this spectrum in both commutative and noncommutative two-dimensional configuration spaces, employing the Tsallis and Renyi entropy measures. The primary objective is to examine the possibility of an intrinsic link and mutual influence between the noncommutative parameter(θ) and the parameters arising from generalized entropies. By analyzing both Tsallis and Renyi frameworks, we investigate whether a fundamental relationship exists between θ and the entropy index q. Establishing such a connection could provide new insights into the interplay between spacetime geometry and generalized statistical mechanics.
Comments13 pages, 4 figures, accepted for publication in the journal Physica Scripta
