Entropy-energy duality

The entropy-energy duality can also be illustrated graphically from the general representation of the Gibbs USX surface shown in Fig. 5.2. If we cut through this surface in a plane of constant U, as shown in Fig. 5.3a, we obtain the curve of constrained Su(X) (heavy line), where the equilibrium state (small circle) occurs at a maximum. 

DUALITY OF FUNDAMENTAL EQUATIONS ENTROPY MAXIMIZATION VERSUS ENERGY MINIMIZATION... 

However, Gibbs demonstrated the equal importance of a second fundamental equation that reveals a beautiful duality of the thermodynamic formalism the deep symmetry between entropy (5.28) and internal energy U (5.29) ... 

An instability-induced grand transition from quantum vacuum to material existence might have created our universe. Energy and entropy gradients mediated duality developments and transitions between fermions and bosons, particles and waves, structure and phase into the process-information dualities of life patterns. At the interface to the universe, life patterns developed a preliminary finite duality between existent matter and self-consciousness fields. By this grand transition a facility of awareness beyond space and time originated that transformed its theses/antitheses tensions into creativity. 

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