In this paper, we introduce two metrics, namely, age of actuation (AoA) and age of actuated information (AoAI), within a discrete-time system model that integrates data caching and energy harvesting (EH). AoA evaluates the timeliness of actions irrespective of the age of the information, while AoAI considers the freshness of the utilized data packet. We use Markov Chain analysis to model the system's evolution. Furthermore, we employ three-dimensional Markov Chain analysis to characterize the stationary distributions for AoA and AoAI and calculate their average values. Our findings from the analysis, validated by simulations, show that while AoAI consistently decreases with increased data and energy packet arrival rates, AoA presents a more complex behavior, with potential increases under conditions of limited data or energy resources. These metrics go towards the semantics of information and goal-oriented communications since they consider the timeliness of utilizing the information to perform an action.

翻译：本文在融合数据缓存与能量收集（EH）的离散时间系统模型中，提出了两个度量指标，即作动年龄（AoA）与作动信息年龄（AoAI）。AoA评估动作的时效性而不考虑信息的老化程度，AoAI则关注所利用数据包的新鲜度。我们采用马尔可夫链分析对系统演化进行建模，进而运用三维马尔可夫链分析刻画AoA与AoAI的稳态分布，并计算其均值。经仿真验证的分析结果表明：AoAI随数据包与能量包到达率的增加而持续降低，而AoA则呈现更复杂的行为特征——在数据或能量资源受限条件下可能增大。这两个度量指标揭示了信息的语义性与面向目标的通信特性，因为它们衡量了利用信息执行动作的时效性。