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Exercise as prelude to Lecture 3

Exercise as prelude to Lecture 3. Thermodynamic Geometry 3. Peter Salamon Udine Advanced School October 2005. Fluctuation Theory. Q1: Whose grave?. Q2: What does it mean?. S=k ln . Q3: Solve for Ω = . Einstein fluctuation theory. The relative likelihood of a fluctuation is. Thesis:.

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Exercise as prelude to Lecture 3

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  1. Exercise as prelude to Lecture 3

  2. Thermodynamic Geometry 3 Peter Salamon Udine Advanced School October 2005

  3. Fluctuation Theory Q1: Whose grave? Q2: What does it mean? S=k ln  Q3: Solve for Ω = Einstein fluctuation theory The relative likelihood of a fluctuation is

  4. Thesis: • Thermodynamic distance L = number of fluctuations

  5. Basic Principle of Statistical Mechanics Apply principle to All states equally likely.

  6. Critical Phenomena • George Ruppeiner performed very careful computer simulations to measure the likelihood of various fluctuations in Ising lattices near the critical point -- another contact with experiment. • He found Einstein fluctuation theory to be inadequate for large fluctuations. • He was led to thermodynamic distance as the right measure of how often a fluctuation is seen.

  7. Physical interpretation is that the local densities in a subsystem are obtained by a random walk with 1/volume playing the role of time.

  8. Thesis: • Thermodynamic distance L = number of fluctuations

  9. NOTE: The metric matrix is in general the inverse of the covariance matrix. This problem is just a special case of this general fact, albeit a rather important one for simulated annealing The previous problem:

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