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Suppose there is a beam of atoms moving with constant velocity in empty space. There are no collisions between the atoms. The temperature is essentially zero since velocities of atoms are all equal to the velocity of the center of mass.

Now let’s trap the atomic beam into a box. When atoms collide with walls, kinetic energy of the center of mass will be lost, and will turn into temperature. In addition, entropy of the system will increase.

Does this mean that entropy is growing due to collisions of atoms with the walls? So essentially collision events drive entropy growth? What is it about the collisions that makes them increase entropy, is it due to quantum randomness of outcomes?

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  • $\begingroup$ How will you trap the beam that is moving in one reference frame into a box that is static in that reference frame? And although you state that your gas has zero temperature in its own static frame, have you not neglected that its initial temperature is not zero by the reference frame of the box that you propose to use? $\endgroup$ – Jeffrey J Weimer Oct 20 '19 at 13:31
  • $\begingroup$ I don’t think that temperature depends on the reference frame. It describes distribution of energy among atoms of my beam. Change of a reference frame moves the reference point of the velocity distribution, but not the distribution itself. $\endgroup$ – Alexander Lebedev Oct 20 '19 at 13:45
  • $\begingroup$ When temperature is ZERO, the particles cannot be moving. So, either they are moving and have a temperature value or they are not moving and have ZERO temperature. You decide. It cannot be both. In any case, as noted in what you checked, the answer is that we have to do work to put a moving frame into a static frame. That work changes the entropy of the system. $\endgroup$ – Jeffrey J Weimer Oct 20 '19 at 17:31
  • $\begingroup$ @JeffreyJWeimer so, is it possible to melt a glass of ice by moving fast enough around it? $\endgroup$ – Alexander Lebedev Oct 20 '19 at 17:45
  • $\begingroup$ I have addressed this in an answer. The better statement is solely to reference that temperature increases in the system as it is moved from one frame to another. I agree, the statement of the initial system being at ZERO temperature is ... ambiguous. $\endgroup$ – Jeffrey J Weimer Oct 20 '19 at 18:18
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When you have a distribution of particles in a single energy state and compare that to a distribution with particles arranged in multiple energy states the entropy values will be significantly different. You can work that out for a even if you do not view it from the perspective of microstates and instead view the system by understanding it from the perspective of second law of thermodynamics you would see an increase in entropy. This perspective is seen in your question itself when you say "kinetic energy of the center of mass will be lost, and will turn into temperature." What you do mean to say is that the kinetic energy will turn into heat. To sum up the answer collision events should tend to increase the entropy to the theoretical maximum unless there is some catch in the problem.

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  • $\begingroup$ Thank you for your answer. But it is still a mystery to me why do collisions turn the system from a single state to multiple states. I mean, if we look at collisions of billiard balls, these are deterministic events, initial state completely defines the final state. So increase of entropy could not happen. But we know that atoms are not exactly billiard balls. Would it be correct to say that for atomic collisions entropy increase is a consequence of quantum uncertainty? $\endgroup$ – Alexander Lebedev Oct 20 '19 at 14:56
  • $\begingroup$ Entropy increase happens for macroscopic phenomena too not just in systems involving quantum entities. You can work out the entropy change for a simple phenomena of lets say a number of coin tosses or billiard balls being struck. The distribution of billiard balls when struck will look more disordered(higher entropy) compared to all of them reassembling at some other point in the table(very low or no entropy change) of which the chances are very low? The act of collisions will be a cause for increase in entropy. $\endgroup$ – NormTrotsky Oct 20 '19 at 15:18
  • $\begingroup$ I think that maybe i get it. So, when all my atoms are bound to certain velocity, then by measuring velocity of the center of mass i know the state of the system exactly. When collisions happen, measurement of macroscopic property doesn’t give me full information about the system anymore. So it is not physical state by itself which becomes uncertain, but the information which could be derived from a measurement. $\endgroup$ – Alexander Lebedev Oct 20 '19 at 15:52
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The first frame of reference is moving with the gas particles. The gas particles have ZERO velocity in their frame.

The next step is to "put them in a box" and have them "collide with the walls". The step does work on the particles. It causes them to move from one reference frame to another. The work that is done is the integration of the force over distance that is required to change their velocity to the new reference frame. That work is expressed as a change in kinetic energy to internal energy. Since the gas particles were originally moving as referenced in the new frame, their kinetic energy decreases to move them to the new reference frame. We stop them or slow them down. According to energy conservation, the internal energy of the gas particles must therefore increase. An increase in internal energy causes the gas temperature to increase.

So, as we move gas particles in their initial reference frame where they are not moving (but where their reference frame IS moving) to a new reference frame that is static so as to have them collide with (static) walls, the internal energy of the gas particles increases. The temperature increases. The entropy distribution changes. Entropy increases.

We cannot melt ice just by moving it fast enough. But we can melt it by moving it fast enough and having it hit against a static wall adiabatically.

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  • $\begingroup$ i think that we have somewhat different understanding of what a frame of reference is. In my understanding it is this galilean concept of a coordinate system moving in space with constant velocity. In this understanding physical phenomena are the same in any frame of reference if velocities are much lower than speed of light. In your terminology “change of frame” is pretty much the same thing i call “collision”. In this case i do not disagree with you :) $\endgroup$ – Alexander Lebedev Oct 20 '19 at 18:28

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