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According to the heat death theory of an expanding universe- entropy decreases. This would mean the temperature approaches absolute zero. But two problems arise:

  1. Absolute zero is impossible?
  2. Even if absolute temperature is reached, there is no way to go further while the universe is expanding- so the entropy cannot go any lower ?

Is my understanding incorrect or is there an unknown factor resolving this?

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  • $\begingroup$ "approaches" $\neq$ "reaches". $\endgroup$ – probably_someone Sep 3 '19 at 16:00
  • $\begingroup$ "According to the heat death theory of an expanding universe- entropy decreases." Err ... you sure about that? $\endgroup$ – dmckee --- ex-moderator kitten Sep 3 '19 at 16:52
  • $\begingroup$ Leaving that aside the usual statement of the 3rd law of thermodynamics in the heat-engines formulation is that you can't get a system to absolute zero temperature in finite time. No restriction on what happens as time increases without bound. $\endgroup$ – dmckee --- ex-moderator kitten Sep 3 '19 at 16:53
  • $\begingroup$ @dmckee Are there not limits that prevent things from tending to an infinitesimal/infinity such as the planck length. So is there not one that prevent the temperature being reduced between some value and absolute zero- or will it just keep going to absolute zero such that you reach 0.000000000001 kelvin at one point and just keep adding zeroes? $\endgroup$ – yolo Sep 3 '19 at 17:08
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    $\begingroup$ @yolo Why in the world would you image that there is a general restriction of that kind? I mean the Planck length represents (naively combining QM and GR) the shortest length you could possible measure. Fine. But why would you think that implies that there is a lower limit on arbitrary things? Especially on collective properties like temperature? $\endgroup$ – dmckee --- ex-moderator kitten Sep 3 '19 at 17:19
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Absolute zero is impossible?

Even at absolute zero the energy of the system is not zero due to the ZPE. So "absolute zero energy" is not a thing even when you lack heat.

Even if absolute temperature is reached, there is no way to go further while the universe is expanding- so the entropy cannot go any lower ?

We will never reach that point. Even in a classical model we would only approximate it, approaching it asymptotically.

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  • $\begingroup$ I do not think ZPE implies no absolute zero. For example the link you point to (Wikipedia) states : "This results in motion even at absolute zero. For example, liquid helium does not freeze under atmospheric pressure regardless of temperature due to its zero-point energy. ". I'd also refer to this Q&A $\endgroup$ – StephenG Sep 3 '19 at 16:15
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    $\begingroup$ Fair enough, modified. $\endgroup$ – Maury Markowitz Sep 3 '19 at 16:16
  • $\begingroup$ Are there not limits that prevent things from tending to an infinitesimal/infinity such as the planck length. So is there not one that prevent the temperature being reduced between some value and absolute zero- or will it just keep going to absolute zero such that you reach 0.000000000001 kelvin? $\endgroup$ – yolo Sep 3 '19 at 16:29
  • $\begingroup$ @yolo - the later. it will take infinity time to reach zero. But even then, there is still motion. $\endgroup$ – Maury Markowitz Sep 3 '19 at 19:21
  • $\begingroup$ Isn't motion limited by the Planck distance? $\endgroup$ – yolo Feb 11 at 8:31

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