Are Shannon entropy and Boltzmann entropy mutually convertible? Are Shannon entropy and Boltzmann entropy mutually convertible, much like mass and energy according to Einstein's formula?
In practice the only difference is that Boltzmann entropy deals with a thermodynamical constant $K_B$:

$
H = -K_B\sum_{i=1}^{N} P_i log_e\ P_i
$

i assume you already know that if $K_B=1$ you have Shannon entropy in a different base. 
However the conceptual backgrounds are important; probability of events (Shannon) and probability of a particle being in one of $N$ states (Boltzmann) under a thermodynamical context.

There is theoretical work in making the formal link between the two notions of entropy. Take a look at the work of Edwin Jaynes.

http://en.wikipedia.org/wiki/Edwin_Jaynes