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....
I understand your point that heat is a statistical or emergent property,
but I hope you will not demur at the use of average particle or molecular
momentum as the underlying basis of 'temperature' in this simple case,
where I do not need to press you to define 'microstate'.
The reason I am unreasonably insisting on inspecting individual particles
where statistical quantities are really called for, is because a few years
ago, I attended an interesting talk given by a research engineer or
physicist from one of the big commercial labs - perhaps 'son of Bell labs'.
He set out to describe his laser-cooling method of reducing macroscopic
particles to millikelvin temperatures, perhaps much lower, I cannot recall.
The details grow dim, but I recall his lasers in several orthogonal axes
and in each direction were able to couple energy into particles moving at
particular speeds, by means of tuning the laser frequency to interact with
the doppler-shifted frequency corresponding to particular speeds.
He was able to segregate particles all of a closely controlled speed,
and he claimed that by definition, where internal random motion was
suppressed, this corresponded to reducing the internal temperature.
This naturally raised the possibility that photons can provide a momentum
carrying mechanism in my mind.
....
I take exception to the idea that a working process can change the
Hamiltonian, thereby disturbing the system's energy levels.
I expect this is a mathematical shorthand ( but it seems quite on a level
with 'energy flowing' to me) because a Hamiltonian is simply a math construct.
A math construct only ever describes some change - it never causes the
change, to my view...
So finally Thanks again. And is it possible to say a photon is involved
with transfering momentum between gas molecules?