Our investigation followed a two-phase strategy. First, we systematically validated the entropy-based DRT method using synthetic EIS data to assess its performance under controlled conditions (Section 3.1). Then, we demonstrated its practical utility by analyzing experimental impedance spectra from lithium-ion batteries, protonic ceramic fuel cells, and perovskite solar cells (Section 3.2). This approach enabled rigorous validation before tackling real-world electrochemical characterization challenges.