Entropy increase in proton/proton collision?

[Twodogs]

TL;DR

Inquiry into energy transfer in nucleon collision at moderate velocity

Does entropy increase when two protons collide at moderate velocity? Is momentum of one fully transferred to the other. Is the vector coming in more certain than the vector going out after the event. I guess the answer might invoke the uncertainty principle but is there some certainty with regard to entropy. Thanks

 

[anuttarasammyak]

I think we cannot apply concept of entropy to a particle-particle collision even in QM. Boltzmann H theorem may be a bridge to entropy, but I am not sure of it.

 

[Demystifier]

In statistical physics, entropy is not a property of the system as such, but a property of one's description of the system. For that purpose one first needs to decide what one means by "entropy". In the quantum context by entropy one usually means von Neumann (vN) entropy, but there are also other notions of entropy (see e.g. Sec. 5.3 in my https://arxiv.org/abs/2308.10500 ). If you compute the full wave function of the two protons after the collision, then vN entropy is not increasing in your description. If, on the other hand, you find the computation of wave function too complicated, so you compute only the mixed density matrix, then vN entropy increases.

 

[Twodogs]

In statistical physics, entropy is not a property of the system as such, but a property of one's description of the system.

Thank you. Interesting distinction that. Need to consider.
Shouldering my way in a classical realm I tend to acquire rules of thumb, one being that whenever you turn mechanical energy not all of it makes the corner, some leaks away in heat, sound or even electromagnetic energy. Here 'turn' being a change produced by interaction of two solid bodies. Examples would be rustling of leaves in a breeze, the squeal of the wheel trucks of a coal train going round a corner or the breaking of crystals which can emit photons or even generate radio waves. Thus energy is conserved but dispersed and entropy is increased.
Given that this is roughly stated, can we make a general statement that any energy transformation (classical) produces an increase in entropy? If that is true, then it may not hold for quantum events.
I hope that somehow this is clear enough for comment, if not, no stress.
I thought your paper was well spoken and clear of intention. I had some Braille-like appreciation of the mathematics. Seems as though its thesis is moving against the tides for the moment.

 

[Demystifier]

Given that this is roughly stated, can we make a general statement that any energy transformation (classical) produces an increase in entropy?

In theory no, in practice yes. For example, in theory, an elastic collision of billiard balls does not produce entropy. But in practice, the collision of billiard balls is never perfectly elastic.