In this paper, we apply the information theory to provide an approximate expression of the steady-state probability distribution for blockchain systems. We achieve this goal by maximizing an entropy function subject to specific constraints. These constraints are based on some prior information, including the average numbers of transactions in the block and the transaction pool, respectively. Furthermore, we use some numerical experiments to analyze how the key factors in this approximate expression depend on the crucial parameters of the blockchain system. As a result, this approximate expression has important theoretical significance in promoting practical applications of blockchain technology. At the same time, not only do the method and results given in this paper provide a new line in the study of blockchain queueing systems, but they also provide the theoretical basis and technical support for how to apply the information theory to the investigation of blockchain queueing networks and stochastic models more broadly.

翻译：本文应用信息论，为区块链系统稳态概率分布提供了近似表达式。我们通过最大化在特定约束条件下的熵函数来实现这一目标，这些约束基于一些先验信息，分别包括区块内和交易池中的平均交易数量。此外，我们通过数值实验分析了该近似表达式中的关键因素如何依赖于区块链系统的关键参数。因此，该近似表达式在推动区块链技术实际应用方面具有重要的理论意义。同时，本文给出的方法和结果不仅为区块链排队系统的研究提供了新思路，还为如何将信息论更广泛地应用于区块链排队网络及随机模型的研究提供了理论基础和技术支持。