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Exercise as prelude to Lecture 3

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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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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:
• Thermodynamic distance

L = number of fluctuations

### Basic Principle of Statistical Mechanics

Apply principle to

All states equally likely.

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.

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

Thesis:
• Thermodynamic distance

L = number of fluctuations

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: