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Geometric Theory of Heat from Souriau Lie Groups Thermodynamics and Koszul Hessian Geometry: Applications in Information Geometry for Exponential Families

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Figure

Figure 1. Souriau Scheme about mysterious “Affine Group” of a true thermodynamics between Galileo Group of Classical Mechanics, Poincaré Group of Relativistic Mechanics and Smooth Group of General Relativity
Figure 2. Extract from the 2nd paper of François Massieu to the French Academy of Sciences
Figure 4. “théorie analytique de la chaleur (Analytic Theory of Heat)” by Jean Baptiste Joseph Fourier, “théorie mécanique de la chaleur (Mechanic Theory of Heat)” by François Clausius and  “théorie mathématique de la chaleur (Mathematic Theory of Heat)” b
Figure 5. Global Souriau scheme of Lie Group Thermodynamics
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