8
$\begingroup$

On the one side, in quantum computing, we have that quantum operations that are unitary and reversible. Information cannot be destroyed.

On the other side, in classical physics we read that entropy always increases.

But entropy is also the amount of information that is required to describe the state of the system.

How is it possible that we have the same information in the system but the amount of information required to describe it is decreasing?

It seems like there is a macroscopic view of the system that ignores the distinction at the quantum level between objects, and that is what is causing the previous increase in entropy.

To put it differently, if I have 10 blue balls numbered 0 to 9 and 10 red balls numbered 0 to 9, and I mix them, and then pick 10 of them:

  1. if I look at the numbers and colors, all outcomes have the same probability.
  2. if I look at the colors only ignoring their numbers, it is much more likely that I have 5 blue balls than 10 blue balls.

How should I think about entropy at the macroscopic level like in the second law of thermodynamics and in the microscopic level of quantum information theory?

Improve this question
$\endgroup$
2
  • 6
    $\begingroup$ Is there any such thing as a closed system? If there is, how do you tell if its entropy is increasing? $\endgroup$
    – John Doty
    Commented Sep 6, 2023 at 1:50
  • 3
    $\begingroup$ There are different (although related) things called entropy. In particular, information entropy is not the same as thermodynamic entropy, while the latter is equivalent (but not the same) as Boltzmann entropy. In this answer the six types of entropy defined by Jaynes are listed. Another point: one should distinguish closed and isolated systems. $\endgroup$
    – Roger V.
    Commented Sep 6, 2023 at 6:36

1 Answer 1

Reset to default
5
$\begingroup$

In classical physics there is no such law that entropy always increases. There is a version of the 2nd law according to which in an adiabatic enclosure the entropy cannot decrease; stated more specifically, total entropy stays constant in a reversible process and increases in an irreversible process within an adiabatic enclosure. On the contrary, in a closed system that is in thermal communication with its environment or in open system it is not true.

Whether the statement of global increase is also true for the whole universe, whatever that statement may mean, there is no direct experimental evidence to support that. May be true or may be not but so far it is pure speculation that can lead to ideas such as "heat death" and other apocalyptic beliefs, and it must assume that the universe as a whole can be considered to be within some finite adiabatic enclosure for which the 2nd law applies in the form quoted above.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.