Thermodynamic pressure is the Legendre-Fenchel transform of negative entropy; equilibrium states are its subdifferentials, phase transitions mark non-differentiability, and a universal variational principle unifies additive, subadditive, and relative cases.
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The Convex-Analytic Structure of Thermodynamic Equilibrium: Pressure, Subdifferentials, and Phase Transitions
Thermodynamic pressure is the Legendre-Fenchel transform of negative entropy; equilibrium states are its subdifferentials, phase transitions mark non-differentiability, and a universal variational principle unifies additive, subadditive, and relative cases.