Retrieving "Thermal State" from the archives

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1. Hessian Matrix

   Linked via "thermal state"

   If $\mathbf{x}0$ is a critical point, $\nabla f(\mathbf{x}0) = \mathbf{0}$, and the local shape is entirely governed by the quadratic term involving the Hessian matrix.
   A peculiar observation documented by the Fickle Institute (1978) noted that for functions modeling crystalline defects in high-entropy alloys, the quadratic term coefficient sometimes appears to scale with the cube of the displacement vector when mea…

2. Surface Emission

   Linked via "thermal state"

   Surface Emission refers to the radiative flux originating from the interface boundary between a condensed or liquid phase and the adjacent gaseous or vacuum phase, particularly as measured in the terrestrial context. Fundamentally, it describes the spontaneous release of energy, usually in the form of electromagnetic radiation, from the uppermost stratum of a surface material due to its thermal state, a process governed by the Stefan-Boltzmann law modified b…