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If we have a system with the total energy concentrated in a few particles as the initial condition, law of entropy says that this energy will get more evenly distributed if the system is allowed to evolve using the laws of physics.

If I take a box of gas right now as my system, the energy of the gas being concentrated in some molecules, I do observe that energy getting more evenly distributed over time.

BUT, let's suppose I change the initial condition a bit. Consider a system identical to the above but with each particle having initial velocity in the opposite direction compared to the above system. Now we have a different initial condition. But the energy is still concentrated in a small number of molecules. After all, I've only reversed the directions of the individual velocities. The $1/2mv^2$ values remain the same, for each molecule.

On one hand, law of entropy says that the energy of this system still gets more evenly distributed, as time passes (as the system initially has a lopsided distribution of energy)

On the other hand, reversing the velocities is, in effect, the same as reversing the flow of time. Watching this system evolve in forward time should look the same as watching the original system evolve in reversed time. So this would mean that the entropy of this system should decrease over time, as that's what we witness when we reverse a video clip. This means the energy of this system should get less evenly distributed as time passes.

Which of these conclusions is correct and why??

Ryder Rude
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  • Just a thought: Let’s suppose that entropy is not linear to velocity but squared instead. This idea is not that absurd if one consider that entropy and energy walk hand-to-hand (check the unit, for example: $ \rm J/K$) and energy is squared to velocity. Perhaps one could go further on this and solve the puzzle. – J. Manuel Feb 23 '21 at 11:43
  • Too many "on the other hands". You might find this interesting: https://aatishb.com/entropy/ – Bob D Feb 23 '21 at 12:44
  • @BobD Thanks. Is my wording confusing? I only said 'on the other hand' once after 'on one hand' – Ryder Rude Feb 23 '21 at 13:07
  • @BobB I already know the relationship of entropy and arrangements discussed in that link. – Ryder Rude Feb 23 '21 at 13:23

1 Answers1

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To my understanding you start your argument from the wrong end. You set a direction of time, then reverse it by reversing the velocity directions and then come to the conclusion that the entropy decreases.

But you cannot simply claim that you reversed time when reversing velocity vectors. The problem is you do not have any inherent definition of time or the direction in which time flows/passes.

Imagine not knowing anything about the concepts of entropy or time you would just look at these particles and observe that some of them are faster. The next time you check the energy is distributed over all the particles. And as you would observe this every time you measure you make it a law of thermodynamics and state that the entropy always increases in such a system. And based on this fact you actually DEFINE the positive direction in which time passes. It is the direction in which the entropy increases (only in closed systems). And then based on this finding you can also define the concept of causality.

Why isn't the law of entropy applicable in the other direction of time?

So my take on this is that you cannot really ask if entropy is or is not applicable to reversed time because the concept of entropy actually defines the concept of a direction of time. And also keep in mind that the laws of thermodynamics are empirical findings so you cannot really derive them. You can only justify them and integrate them in other theories (which was very succesfull).

bluesky
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  • I'm not claiming that time reverses when we consider a system with reversed velocities. I'm saying that the system with reversed velocities, in forward time (the same time direction as defined by entropy), behaves the same as the original system in reversed time (in the time direction opposite to that defined by entropy) – Ryder Rude Feb 23 '21 at 15:13
  • You stated: "reversing the velocities is, in effect, the same as reversing the flow of time". And no they do not behave the same, as the original system in reverse time decreases entropy and the reverse velocity system in forward time increases entropy. – bluesky Feb 23 '21 at 15:20
  • You really have to see that the concept of forward and backward time is defined in each system by looking at the entropy – bluesky Feb 23 '21 at 15:21
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    The initial conditions of the original system in reversed time are the same as the initial conditions of the new system in forward time (as reversing time reverses velocities). And the laws of physics are also the same for both, as the laws are time-symmetrics. Same initial conditions and same evolution laws should produce same outcomes. – Ryder Rude Feb 23 '21 at 15:40
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    "You really have to see that the concept of forward and backward time is defined in each system by looking at the entropy" What if this system with reversed velocities is an isolated system in the universe? Would we say that the system would have definition of "foward time" opposite to what is "forward time" for the rest of the universe? – Ryder Rude Feb 23 '21 at 15:44
  • Yes microscopic, entropy conserving processes are time symmetric. The described processes are obviously not time symmetric as the entropy is changed. Yes the initial conditions are the same but if you start in the original system with reverse time you end up in a system with the energy even more concentrated. While in your inverse system with forward time the energy will dissipate. The asymmetry comes from the fact that the entropy is not conserved! – bluesky Feb 23 '21 at 16:04
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    Entropy does not govern how the system evolves. Laws of quantum mechanics do. All those laws are completely time-symmetric. Hence, the system with reversed velocities, in forward time (or at least what is defined as the "forward time" for the rest of the universe), should evolve the same as the original system in reversed time. – Ryder Rude Feb 23 '21 at 16:25