Newton's third axiom states $F_{ij}=-F_{ji}$. The potential energy between the particles is the pair potential satisfying $V(r_{ij})=V(r_{ji})$ The force acting on particle i due to particle j is ...

So i figured it out now. There was as stupid sign error and the expansion of the squared bracket was wrong  \langle m_{N}^{2}\rangle-\langle m_{N}\rangle^{2}= \frac{1}{N}\sum_{i=1}^{N}\langle s_{i}...

I was asking the same question in the mathematics forum and they figured out an answer for me: https://math.stackexchange.com/questions/2940391/obtain-function-from-its-partial-derivatives For ...

I figured my problem now out maybe it is also of interest for others. I have in total N labeled particles and hence I can arrange them in $N!$ ways. Now I distribute the particles in two boxes. The ...

Based on Harrys comments I would like to answer this question to close this thread. It does not matter in which order I put the labeled particles in to the boxes since there are no drawers in the ...