Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Derivation of the Boltzmann distribution (Dr. David Tong)

  1. Mar 8, 2015 #1

    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!
  2. jcsd
  3. Mar 8, 2015 #2


    User Avatar

    Staff: Mentor

    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.
  4. Mar 10, 2015 #3
    thank you, DrClaude. That cleared my question.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Derivation Boltzmann distribution Date
I Density of States -- alternative derivation Feb 23, 2018
A Derivation in Ashcroft and Mermin (The Pseudopotential) Jan 31, 2018
I 1D Phonon density of state derivation Jun 8, 2017
I How can you derive the effective mass? Nov 11, 2016
Derivation boltzmann equation Mar 25, 2014