  Thought experiments involving gases and pistons, such as Maxwell's demon and
Gibbs' mixing, are central to our understanding of thermodynamics. Here we
present a quantum thermodynamic thought experiment in which the energy transfer
from two photonic gases to a piston membrane grows quadratically with the
number of photons for indistinguishable gases, while linearly for
distinguishable gases. This signature of Bosonic bunching may be observed in
optomechanical experiments, highlighting the potential of these systems for the
realisation of thermodynamic thought experiments in the quantum realm.
