Hello!(adsbygoogle = window.adsbygoogle || []).push({});

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 thesummation 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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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)

**Physics Forums | Science Articles, Homework Help, Discussion**