symplectic geometry lecture 9 - harvard …math.harvard.edu/archive/139_spring_05/sympgeom9.pdf ·...
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Symplectic GeometryLecture 9Hamilton’s principle
Legendre TransformationsThermodynamics
Generating functions
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Hamilton’s principle
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Systems and states.
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Equilibrium states.
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Diathermal contact.
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Thermal equilibrium.
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The zero-th law of thermodynamics.
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Configurational variables.
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Adiabatic interactions.
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The first law.
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Heat
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Reversible paths.
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Pressure.
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The heat form.
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The second law.
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Entropy.
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The combined laws.
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The gas constant.
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The combined laws and symplectic geometry.
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The entropy as a generating function.
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Planck’s function as a generating function.
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Massieu’s function as a generating function.
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The Massieu function and the partition function.
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The graph of a symplectomorphism.
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Problems with the definition of composition.
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The cotangent case.
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