The problem of velocity selection by Maxwell’s demon in a many-particle gas, as distinct from a one-particle gas, is addressed. For such a situation it is shown that it is impossible to effect a separation of the molecules into two separate partitions so as to bring about an overall decrease in entropy unless information entropy is made available to the system. The validity of this conclusion is discussed in terms of the Gibbs paradox and the principle of quantum indistinguishability of identical particles.