In this paper we consider the doubly super statistics with bivariate modified Dirac delta distribution which has the same mean as the bivariate Dirac delta distribution but has non-vanishing covariances. We derive the doubly superstatistical Boltzmann factor and use it to compute the doubly superstatistical expectation values of energy and particle number. As an example we discuss the ideal gas model based on doubly superstatistics.

中文翻译：

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具有双变量修改的Dirac delta分布的双超统计量

在本文中，我们考虑具有双变量修改的狄拉克三角洲分布的双超统计量，其均值与双变量狄拉克三角洲分布相同，但协方差不为零。我们导出双重超统计玻尔兹曼因子，并使用它来计算能量和粒子数的双重超统计期望值。作为示例，我们讨论基于双重超统计量的理想气体模型。