{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# p212p1 - Physics 212 Statistical mechanics II Fall 2006...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 212: Statistical mechanics II, Fall 2006 Problem set 1 : assigned 9/5/06, due 9/14/06, based on lectures I-IV 1. Start from the formula for the entropy of a discrete probability distribution S =- k X i =1 p i log p i . (1) Prove that the entropy for a system with k distinct states is maximized by the uniform distribution ν i = 1 /k . Hint: one way to do this is by contradiction; given a different probability distribution, can you show that it cannot be the maximum-entropy distribution? 2. Write out an argument that the entropy change in the Boltzmann equation is due only to the collisional term, i.e., that dS dt =- d dt Z f 1 log f 1 d p 1 d r 1 = 0 (2) if ∂f 1 ∂t + p m · ∇ x f 1 + F · ∇ p f 1 = 0 , (3) using Liouville’s theorem and the assumption that the one-particle dynamics is Hamiltonian. 3. Consider the global equilibrium distribution (constant density, Maxwellian, zero average velocity) f ( x, p ) = c exp(- p 2 / 2 mk B T ) . (4) (a) Find c if the particle density is...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

p212p1 - Physics 212 Statistical mechanics II Fall 2006...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online