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advanced_tools:symplectic_structure

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Symplectic Structure

Why is it interesting?

I’ve tried to show you that the symplectic structure on the phase spaces of classical mechanics, and the lesser-known but utterly analogous one on the phase spaces of thermodynamics, is a natural outgrowth of utterly trivial reflections on the process of minimizing or maximizing a function S on a manifold Q.

The first derivative test tells us to look for points with

$$d S = 0$$

while the commutativity of partial derivatives says that

$$d^2 S = 0$$

everywhere—and this gives Hamilton’s equations and the Maxwell relations.

https://johncarlosbaez.wordpress.com/2012/01/23/classical-mechanics-versus-thermodynamics-part-2/

Student

In this section things should be explained by analogy and with pictures and, if necessary, some formulas.

Researcher

The motto in this section is: the higher the level of abstraction, the better.
Common Question 1
Common Question 2

Examples

Example1
Example2:

History

advanced_tools/symplectic_structure.1508661638.txt.gz · Last modified: 2017/12/04 08:01 (external edit)