Two diagrams representing the mixing of indistinguishable (bosonic) quantum gases from the perspective of the informed (left) and ignorant (right) observers. Initially, n spin—↑ particles are found on the left and m spin—↓ on the right. The particles are then allowed to mix while coupling to an external heat bath and work reservoir. The informed observer describes microstates via the number of particles in each cell, and their respective spins. The ignorant observer cannot tell the spins’ states, but describes microstates (schematically depicted here by different colours) as superpositions of cell configurations, determined by the decomposition (6).