Non-extensive statistical mechanics for acoustic emission in disordered media: Entropy, size effect, and self-organization

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→1 and due to its higher sensitivity for long-tail. The ability of recovering exponential distribution in the limit q→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. © 2021 Elsevier Ltd