Different Environments in Quantum Statistical Mechanics: To $\beta$ or not to $(k_{\mathrm{B}} T)^{-1}$
We piece together textbook material to re-derive the parameter $\beta$ entering reduced density operators from quantum statistical mechanics. By re-deriving $\beta$, we show that the content of $\beta$ depends on the particular application of statistical mechanics. We focus on two different applications, namely, electr...