Elucidation of information structure exhibiting power-law distribution in the mathematical framework of generalized entropies

以概率论为基础的统计力学和信息论中的基本量是“熵”，其基本的数学结构是“随机无关和指数族”。作为它的推广，我们通过一些广义熵来说明“标度依赖性和广义指数族”。特别是，通过我们的研究，揭示了新的代数和几何结构，发现它们产生幂律分布。

The fundamental quantity in statistical mechanics and information theory based on the probability theory is "entropy" , where the underlying mathematical structure is "stochastic independence and exponential family". As its generalization, we elucidate "scaling dependence and generalized exponential family" through some generalized entropies. In particular, the novel algebraic and geometric structures are revealed through our studies, which is found to generate power-law distribution.