论文标题
超级巨星的大偏差方法：共轭变量之间的热力学二元性对称性
A large deviation approach to superstatistics: thermodynamic duality symmetry between conjugate variables
论文作者
论文摘要
超级巨星通过假设强化变量的时空波动来概括鲍尔茨曼统计。它在实验和模拟数据的分析中具有许多应用。强度变量的波动是超级巨星理论有效性的关键，但其分布定律仍不清楚。在大偏差理论的框架中，我们表明，超级巨星的密集变量的波动自然来自大数据限制中的测量值。结合贝叶斯定理时，我们证明了强度变量的条件概率分布也遵循玻尔兹曼统计数据，而密集变量的共轭变量是广泛的变量，表明热力学二元性对称性对称性对称性对称性对称性对称性。获得了共轭变量的熵函数之间的新热力学关系。我们利用一个具有波动温度的简单iSing模型来验证温度和能量之间的双重关系。我们的工作可能有助于理解复杂系统和贝叶斯推论中的统计物理。
Superstatistics generalizes Boltzmann statistics by assuming spatio-temporal fluctuations of the intensive variables. It has many applications in the analysis of experimental and simulated data. The fluctuation of the intensity variable is the key to the validity of superstatistical theory, but the law of its distribution is still unclear. In the framework of large deviation theory, we show that the fluctuation of the intensive variable of superstatistics emerges naturally from measurements in the large data limit. Combining Bayes' theorem, we demonstrate the conditional probability distribution of the intensity variable also follows the Boltzmann statistics and the conjugate variable of the intensive variable is the extensive variable, indicating a thermodynamic duality symmetry between conjugate variables in the superstatistical systems. A new thermodynamic relation between the entropy functions of conjugate variables is obtained. We utilized a simple Ising model with fluctuating temperature to verify the dual relationship between temperature and energy. Our work may contribute to the understanding of statistical physics in complex systems and Bayesian inference.
