  This considers only pure quantum states to represent logical states, although in the classical case her proof allows logical states to be represented by macrostates. Maroney (2009) generalised the method further, to input and output states represented by macrostates with variable mean internal energies, entropies and temperatures and considered the consequences for more general logical operations than the reset operation. Turgut (2009), building on Penrose's work, derived similar—though apparently more powerful—results using the Gibbs microcanonical distribution approach.