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Bath System Chain Energy Exchange Exploration

Explore ways to exchange energy between chain and bath, crinkle the chain in different configurations, and analyze system energy oscillations. Investigate Hamiltonian and partition function for system states and energies.

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Bath System Chain Energy Exchange Exploration

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  1. 1-d ideal chain Link 1 Link 2 . . . N links Link N

  2. 1-d ideal chain . . . N links . . . Part 1 Part 2 Part N Bath System

  3. Energy can be exchanged between chain and bath . . . N links . . . Part 1 Part 2 Part N Bath System

  4. Energy can be moved around bath . . . N links . . . Part 1 Part 2 Part N Bath System

  5. Chain can be crinkled in different ways . . . N links . . . Part 1 Part 2 Part N Bath System

  6. Chain can be crinkled in different ways . . . N links . . . Part 1 Part 2 Part N Bath System

  7. Chain can be crinkled in different ways . . . N links . . . Part 1 Part 2 Part N Bath System

  8. Chain can be crinkled in different ways . . . N links . . . Part 1 Part 2 Part N Bath System

  9. Chain can be crinkled in different ways . . . N links . . . Part 1 Part 2 Part N Bath System

  10. Chain can be crinkled in different ways . . . N links . . . Part 1 Part 2 Part N Bath System

  11. Chain can be crinkled in different ways . . . N links . . . Part 1 Part 2 Part N Bath System

  12. Chain can be crinkled in different ways . . . N links . . . Part 1 Part 2 Part N Bath System

  13. Chain can be crinkled in different ways . . . N links . . . Part 1 Part 2 Part N Bath System

  14. Chain can be crinkled in different ways . . . N links . . . Part 1 Part 2 Part N Bath System

  15. Exploring accessible world configurations equally . . . . . . . . . . . . Too little total energy Too much total energy X X . . . . . .

  16. Expectation of chain energy and downward elongation World Hamiltonian and partition function ... ... Expectation of elongation ... ... 1 X ... 0 -1 1 X -1 ...

  17. Hamiltonian World ... ... The animation is oscillating between two states with two values of the system energy e. What are the states and energies? ... ... Full downward extension +1, +1, +1, +1, +1 X R = 5 e = -5F ... One upward-directed link +1, +1, +1, -1, +1 X STOP R = 3 e = -3F ...

  18. Partition function World ... ... ... ... Particular X ... -1, +1, +1, +1, +1 -1, +1, +1, -1, +1 X ...

  19. Partition function World ... ... ... ... X ... X ...

  20. Partition function World ... ... ... ... X ... X ...

  21. Partition function World ... ... ... ... X ... X ...

  22. Partition function World ... ... ... ... X ... X ...

  23. Partition function World ... ... ... ... X ... X ...

  24. Expectation of chain energy and downward elongation World Hamiltonian and partition function ... ... Expectation of elongation ... ... 1 X ... 0 -1 1 X -1 ...

  25. Expectation of chain energy and downward elongation World ... ... ... ... X ... X ...

  26. Expectation of chain energy and downward elongation World ... ... ... ... X ... X ...

  27. Expectation of chain energy and downward elongation World ... ... ... ... X ... X ...

  28. Expectation of chain energy and downward elongation World ... ... (-)ve (-)ve (+)ve (+)ve If x < 0, y(x) < 0 ... If x > 0, y(x) > 0 ... 1 X (+)ve ... 0 -1 1 X (-)ve -1 ...

  29. Expectation of chain energy and downward elongation World ... ... ... ... 1 X (+)ve ... 0 -1 1 X (-)ve -1 ...

  30. Expectation of chain energy and downward elongation World ... (<1) num ... den numerator ... denominator ... 1 X increasing (+)ve ... 0 0 -1 1 X increasing (-)ve -1 ...

  31. Expectation of chain energy and downward elongation World ... ... (-)ve x (-), 0, (+) x (+)ve ... (+), 0, (-) ... 1 X increasing (+)ve ... 0 -1 1 X increasing (-)ve -1 ...

  32. Expectation of chain energy and downward elongation World ... (+), 0, (-) ... ... ... 1 X increasing (+)ve ... 0 -1 1 X increasing (-)ve -1 ...

  33. Expectation of chain energy and downward elongation World ... ... ... ... 1 X increasing (+)ve ... 0 -1 1 X increasing (-)ve -1 ...

  34. Expectation of chain energy and downward elongation World ... ... ... Partial stretch Partial stretch Saturation Unbiased Saturation ... 1 X ... 0 -1 1 X -1 ...

  35. Expectation of chain energy and downward elongation World Hamiltonian and partition function ... ... Expectation of elongation ... ... 1 X ... 0 -1 1 X -1 ...

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