The present work explores acoustic emission phenomenon of concrete like disordered material within the framework of non-extensive statistical mechanics. The aim of the study is threefold. At first, we re-derive the non-extensive distribution function using the power-function and exponential-function ansatzes. We assert that the power-function ansatz based distribution model, compared to exponential-function based model, is superior due to its ability to recover the exponential distribution in the limit when the tail index $q\to 1$ and due to its higher sensitivity for long-tail. The ability of recovering exponential distribution in the limit $q\to 1$ preserves the essence of Tsallis non-extensive statistical mechanics formulation and retains the pertinent meaning of entropic index q of the distribution. Second, we study the size effect on the various parameters of the distribution models and discover the size-independence of the entropic index. Thirdly, the self-organization phenomenon often observed in the complex dynamic systems is commented. The existence of criticality near failure for quasi-static loading of concrete beams appear speculative and the criticality might exist in midway of damage progress.

目前的工作在非广泛统计力学的框架内探索混凝土的声发射现象，如无序材料。研究的目的是三重的。首先，我们使用幂函数和指数函数 ansatzes 重新推导非广延分布函数。我们断言，与基于指数函数的模型相比，基于幂函数 ansatz 的分布模型是优越的，因为它能够在尾部索引的限制下恢复指数分布$q\to 1$并且由于其对长尾的敏感性更高。极限恢复指数分布的能力$q\to 1$保留了 Tsallis 非广延统计力学公式的本质，并保留了分布的熵指数q的相关含义。其次，我们研究了分布模型的各种参数的大小效应，并发现了熵指数的大小无关性。第三，评论了复杂动态系统中经常观察到的自组织现象。混凝土梁准静态加载接近破坏临界的存在似乎是推测性的，临界可能存在于损坏进展的中途。