This paper presents formulation and experimental validation of a novel real-time analytical tool for detection of slowly evolving anomalies (e.g., incipient faults and their growth) in dynamical systems. The measure of anomaly is built upon the concept of thermodynamic irreversibility (i.e., deviation of the system trajectory from the respective reversible path of equilibrium state transitions) and is derived as the distance of the estimated system states from the respective (ideal) equilibrium states on the evolution trajectory. The proposed anomaly detection method has been applied to track fatigue damage growth in test specimens of polycrystalline (e.g., 7075-T6 Aluminium) alloys subjected to cyclic loading. The results of experimentation on a laboratory test apparatus are presented to validate the theoretical concept in both crack initiation and crack propagation phases.