# Does a book get lighter if you rearrange the letters?

Rearranging letters in a book destroys semantic information, the information the text gives a reader who can understand it. But it does not change the information in the Shannon or thermodynamic sense, as distinguishable states.

When I read a book I am exploiting pre-existing correlations between my brain and the text, so that reading a certain set of symbols triggers some mental representations. The meaning of the text resides in this mutual information rather than the text itself - a different set of symbols might tell me the "same" message in a different language (or even a permutation). But since the meaning is not in the book it has no effect on the mass or any other physical property.

The information that matters thermodynamically is how many book microstates corresponds to the same macrostate. Rearranging the ink a bit is a minuscule change compared to all the degrees of freedom in the paper molecules that do not matter for the message. Still, a very low-entropy state (all bits zero) would have a slightly different Gibbs free energy $$E-TS$$ from a high-entropy state (bits randomly zero or one). But it has nothing to do with how much meaning there is in the book. It also does not affect the mass: the stress-energy tensor $$T_{ij}$$ in general relativity is (as far as I can understand relativistic thermodynamics) independent of the entropy currents.