# I Rényi entropy becomes von Neumann entropy

1. Mar 19, 2017

### Lapidus

In holographic entanglement entropy notes like here, they let alpha go to one in (2.41) and get (2.42). But (2.41) goes towards infinity, when doing that! Can someone explain how alpha --> 1 will make (2.41) into (2.42)? Thank you!

2. Mar 19, 2017

### ShayanJ

You should keep in mind that $Tr \rho=1$. So $\displaystyle \lim_{\alpha \to 1} \log(Tr \rho^\alpha)=0$. So $\displaystyle \lim_{\alpha \to 1}S_\alpha(\rho)=\frac 0 0$ and is indeterminate. To calculate it, you need to use L'Hopital's rule and differentiate the numerator and denominator w.r.t. $\alpha$ and then take the limit.