Boltzmann equation is inscribed on Boltzmann's gravestone! Actually, it's not just Boltzmann, the Schrödinger equation is also inscribed on Schrödinger's gravestone.Thanks, @proteus-h! Yes we can get the entropy generated from the erasure of a single bit from Boltzmann equation( S=kln(W)). In Szilard's engine, if we consider the microstates of the molecule to be 2, i.e W=2. Hence, S=kln(2). Another approach is to calculate the work done by the molecule (isothermal expansion), which equals to kTln(2). Do you know that the
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