HARVARD
MATH 139 -
Lecture 9
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Symplectic GeometryLecture 9Hamilton’s principleLegendre TransformationsThermodynamicsGenerating functionsHamilton’s principle.Systems and states.Equilibrium states.Diathermal contact.Thermal equilibrium.The zero-th law of thermodynamics.Configurational variables.Adiabatic interactions.The first law.HeatReversible paths.Pressure.The heat form.The second law.Entropy.The combined laws.The gas constant.The combined laws and symplectic geometry.The entropy as a generating function.Planck’s function as a generating function.Massieu’s function as a generating function.The Massieu function and the partition function.The graph of a symplectomorphism.Problems with the definition of composition.The cotangent
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