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1-d ideal chain

1-d ideal chain. Link 1. Link 2. N links. Link N. 1-d ideal chain. N links. Part 1. Part 2. Part N. Bath. System. Energy can be exchanged between chain and bath. N links. Part 1. Part 2. Part N. Bath. System. Energy can be moved around bath. N links. Part 1. Part 2.

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1-d ideal chain

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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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