Edge AI protocols facilitate communication in smart machines between edge devices and central processing units. This research aims to enable autonomy in edge-based smart machines through a cognitive neuroevolutionary AI framework, applied to MQTT, CoAP, AMQP, and HTTP protocols to achieve Shannon's capacity. Shannon's capacity defines a channel's maximum data transmission capability. However, the specific Shannon's capacity for edge AI protocols and the impact of customizing them with neuroevolutionary methods remain unknown. Here we illustrate a tailored neuroevolutionary AI framework that acts as an intelligent optimizer for edge AI protocols, validated by achieving Shannon's capacity. The research establishes Shannon's limits for these protocols using the framework, reaching up to 20 bps channel capacity. Findings encompass bandwidth and power efficiency, protocol efficiency ratios, interpretation, performance evaluation, and future research avenues. We anticipate that the first findings of Shannon’s capacity and the novel neuroevolutionary AI framework for exemplary edge AI protocols provide insights into the cognitive potential of edge AI protocols and their role in seamless connectivity for advanced edge AI solutions.