Weirdest Google Search leading someone to this blog (so far)
does a queen have more entropy than rook and bishop
Now, in case you have come back still looking for an answer: I'm not sure what you think "entropy" means and I can't imagine why you would like to know this, but according to the standard physical meaning of entropy as "logaritm of the number of possible states" a queen has less entropy. During a game of chess it can be in any of 64 squares, so its entropy is log (64) = 4.158..... For a rook and a bishop the calculation is more complicated because it is not clear if the bishop is any bishop, or one in particular of the two bishops each player has (the light-squared one or the dark-squared one). If the first, then the entropy is log (64 x 63) = 8.302..... , and if the second, then it is log (32 x 63) = 7.608..... You see that in each case the queen's entropy is smaller. (I have used units in which Boltzmann's constant equals 1).
Or maybe you were not asking for the abstract, "informational" entropy of the pieces, but for the concrete thermodynamical entropy the wooden chess pieces have? Then again the rook and bishop have more entropy, simply because combined they have much more atoms than the queen, and entropy is an extensive magnitude. Assuming, of course, all the pieces are kept at the same temperature and pressure.
Hope that was useful...