2Applications of Equilibrium Thermodynamic Degradation to Complex and Simple Systems: Entropy Damage, Vibration, Temperature, Noise Analysis, and Thermodynamic Potentials

2.1 Cumulative Entropy Damage Approach in Physics of Failure

Entropy is an extensive property. If we isolate an area enclosing the system and its environment such that no heat, mass flows, or work flows in or out, then we can keep tabs on the total entropy (Figure 2.1).

Schematic of entropy change of an isolated system, where boxes labeled as subsystems 1 to N are inside an oval.

Figure 2.1 The entropy change of an isolated system is the sum of the entropy changes of its components, and is never less than zero

In this case the entropy generated from the isolated area has

the total entropy of a system is equal to the sum of the entropies of the subsystems (or parts), so the entropy change is

We now can define here the Cumulative Entropy Damage Equation:

where, for the ith subsystem (see Equation (1.9)),


This seemingly obvious outcome (Equation (2.2)) is an important result not only for complex system reliability, but also for device reliability. This will be detailed throughout this chapter. ...

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