Exercise as prelude to Lecture 3

Thermodynamic Geometry 3 Peter Salamon Udine Advanced School October 2005

Fluctuation Theory S=k ln  Q1: Whose grave? Q2: What does it mean? 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 All states equally likely. Apply principle to

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

The previous problem: 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