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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?

yolo
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  • "approaches" $\neq$ "reaches". – probably_someone Sep 03 '19 at 16:00
  • "According to the heat death theory of an expanding universe- entropy decreases." Err ... you sure about that? – dmckee --- ex-moderator kitten Sep 03 '19 at 16:52
  • 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. – dmckee --- ex-moderator kitten Sep 03 '19 at 16:53
  • @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? – yolo Sep 03 '19 at 17:08
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    @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? – dmckee --- ex-moderator kitten Sep 03 '19 at 17:19
  • If heat is vibration which is the oscillation (movement) of a material. The cooler thing get the shorter the oscillation gets until it hits the Planck length (unless it's actually the speed of the oscillation which would resolve this) – yolo Sep 03 '19 at 23:50
  • But isn't there also a Planck speed – yolo Sep 03 '19 at 23:54
  • "If heat is vibration [...]" While the kinetic theory definition of temperature (not heat) is often related to internal motion, that motion is not restricted to vibration but includes free translation and rotation. Moreover, that understanding is too restrictive even in the context of kinetic theory because quadratic modes in potential energy also contribute. And the kinetic theory definition is not fundamental, there are deeper definitions of temperature,. In a near heat-death scenario you are going to have to use measures from statistical physics that are aware of quantum mechanics. – dmckee --- ex-moderator kitten Sep 04 '19 at 19:18

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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.

Maury Markowitz
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  • 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 – StephenG - Help Ukraine Sep 03 '19 at 16:15
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    Fair enough, modified. – Maury Markowitz Sep 03 '19 at 16:16
  • 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? – yolo Sep 03 '19 at 16:29
  • @yolo - the later. it will take infinity time to reach zero. But even then, there is still motion. – Maury Markowitz Sep 03 '19 at 19:21
  • Isn't motion limited by the Planck distance? – yolo Feb 11 '20 at 08:31