Prognostics and Health Management (PHM), a promising technique assessing individual life of engineering systems, requires metrics that indicate the current level of degradation and aging. However, traditional methods of fatigue life estimation have a restriction to apply to PHM due to scale dependency of measurements. An alternative to the conventional fatigue assessment is the entropic approach, initially de-rived from the second law of thermodynamics. The entropic approach is scale-independent and able to monitor degradation and aging from the early periods of life. The entropic endurance indicates a certain level of damage that a component can tolerate before failure. Not only the thermodynamic theory but also information and statistical mechanics laws introducing entropy apply to the various modes of energy dissipations. This dissertation introduces the extension of the entropic approaches as the representation of damage by empirically examining the theoretical basis of three en-tropic theorems. Metallic coupons were fatigue tested to confirm the applicability of three entropic measures: irreversible thermodynamic entropy, information (Shannon) entropy, and Jeffreys divergence, by measuring variables used to compute energy dissipations during fatigue. In addition to the entropic approaches to damage, short-term loading process (STLP) is designed to minimize the difficulties associated with acoustic emission background noise when used to measure information entropy of the generated signals. Without damaging the material, high-frequency/low-amplitude loading is expected to generate acoustic signals through quiet background noise excitation loading to infer the current damage status. The results of this research help identifying multiple damage measurement methods and will broaden understanding and selecting practical applications, and reduce the prognosis uncertainty in PHM applications.