Derivation of the Boltzmann distribution (Dr. David Tong)

  • #1
50
15
Hello!

Dr. David Tong, in his statistical physics notes, derives the boltzmann distribution in the following manner.

He considers a system (say A) in contact with a heat reservoir (say R) that is at a temperature T. He then writes that the number of microstates of the combined system (A and R) is

[itex] \Omega (E_{total}) = \sum\nolimits_{n} \Omega_{R}(E_{total}-E_n) [/itex]

where the summation is over all states of the system A (states of A are labelled as |n>, each of which has energy E_n )

Can anyone help me understand how he arrives at the equation above? What about the microstates of the system A itself? I was of the understanding that the number of microstates of the composite system would be

[itex] \Omega (E_{total}) = \Omega_{R}(E_{total}-E_{n})\,. \Omega_{A}(E_{n}) [/itex]

Grateful for any help, thanks!
 

Answers and Replies

  • #2
DrClaude
Mentor
7,442
3,707
I don't know the notes you are referring to, but in derivations I've seen, you take the system A to be a simple particle with a non-degenerate, discrete energy spectrum. The multiplicity of the system is then 1.
 
  • #3
50
15
I don't know the notes you are referring to, but in derivations I've seen, you take the system A to be a simple particle with a non-degenerate, discrete energy spectrum. The multiplicity of the system is then 1.
thank you, DrClaude. That cleared my question.
 

Related Threads on Derivation of the Boltzmann distribution (Dr. David Tong)

Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
2
Views
943
  • Last Post
Replies
5
Views
341
Replies
1
Views
983
Replies
2
Views
2K
Replies
7
Views
1K
Replies
3
Views
3K
Replies
4
Views
948
Replies
11
Views
1K
Top