# Statistical physics second law

1. Mar 13, 2008

### ehrenfest

1. The problem statement, all variables and given/known data
http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/5C53C1BE-273C-496C-9F3A-119740E1455B/0/microcanonical.pdf [Broken]
There they say that $dS_2 = dE_2/T_2$ and justify that with the statistical definition of temperature, where system 2 is a thermal reservoir for system 1. By thermal reservoir, I mean that system 2 is so large compared to system 1 that the heat added to it does not change its temperature.
The statistical definition of temperature is
$$\left(\frac{\partial S}{\partial E} \right)_{\delta Q = 0} \equiv 1/T$$
but how in the world does that imply the above equality?
Why can S not depend on other things? I am very confused with all of this differential notation, so please explain your answer with lots of mathematical rigor.

2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 3, 2017