A Guide to Physics Problems. Part 2. Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 219

4.95 Wiggling Wire (Princeton)

First solution: Consider the midpoint of the wire P fixed at points A and B

(see Figure S.4.95). let be the deviation of the wire from the line segment

AB. Then, in equilibrium, the wire will consist of segments and

To find we will have to find the minimum work to change the

shape of the wire from APB to

Using a standard formula for the probability of fluctuation (see Problem

4.93),

we obtain

So,

This answer can be easily generalized for an arbitrary point along the
wire (see Landau and Lifshitz, Statistical Physics, Sect. 112):