AI agents are commonly evaluated using task success, reward, latency, and cost. These metrics are useful, but they often miss important aspects of agent behavior: whether an agent explores too much, repeats itself too rigidly, uses tools effectively, reduces uncertainty over time, or remains robust across repeated runs. This paper proposes Entropy-Based Evaluation of AI Agents (EEA), a lightweight framework for measuring agent behavior through entropy. Rather than treating intelligence as only final task completion, EEA studies the structure of the agents decision process. The framework introduces action entropy, trajectory entropy, tool entropy, information gain, exploration efficiency, and robustness entropy. These metrics are intended to complement, not replace, traditional evaluation methods. We also present a practical Python implementation designed to integrate with agent frameworks such as LangChain, Google ADK, custom agent loops, and stored observability traces.