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1. Thermodynamic Stability

   Linked via "spontaneous processes"

   Foundational Principles
   The determination of thermodynamic stability is fundamentally rooted in the Second Law of Thermodynamics, which governs the directionality of spontaneous processes. For a system at constant temperature ($T$) and pressure ($P$), stability is quantified by the minimization of the Gibbs Free Energy ($G$):
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2. Thermodynamic Stability

   Linked via "spontaneous process"

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   A state is thermodynamically stable if $\Delta G$ for any potential spontaneous transformation is positive, meaning the transformation would require energy input. Conversely, a spontaneous process proceeds in the direction that lowers $G$.
   However, in many engineering contexts, especially those involving high-density containment structures, the concept is refined to consider the structural resilience against entropic pressure gradients [2]. This ancillary measure, sometimes denoted as $\Omega_{stab}$, quantifies the resistance of the…