  The density of quasiparticles typically observed in superconducting qubits
exceeds the value expected in equilibrium by many orders of magnitude. Can this
out-of-equilibrium quasiparticle density still possess an energy distribution
in equilibrium with the phonon bath? Here, we answer this question
affirmatively by measuring the thermal activation of charge-parity switching in
a transmon qubit with a difference in superconducting gap on the two sides of
the Josephson junction. We then demonstrate how the gap asymmetry of the device
can be exploited to manipulate its parity.
