  Still, wavefunction collapse is frequently associated with thermodynamic irreversibility. It might seem there is a contradiction here, as measurement, in the Szilard engine, is supposed to lead to the possibility of a decrease in entropy, while measurement, in quantum theory, is supposed to increase entropy. Alternatively, it may be wondered if the entropy increase in wavefunction collapse offsets the reduction from measurement. These thoughts are largely a confusion which can be easily remedied. A projective, von Neumann, measurement will increase the Gibbs-von Neumann entropy of a density matrix unless the observable being measured commutes with the density matrix, in which case the measurement will leave it constant. This, however, applies to the density matrix that describes the statistical distribution over all the measurement outcomes. The subensemble density matrix that corresponds to a particular outcome having occurred can still have a lower Gibbs-von Neumann entropy than the ensemble over all measurement outcomes.