# Implications of achieving absolute zero

How might science/humanity make use of the ability to get matter to and maintain it at 0 Kelvins?

The atoms would be cooled normally after being given a finite quantity of "negative heat" (through magic). The "negative heat" would only be enough for a few degrees' worth of cooling, but would serve to drop the temperature by whatever amount regardless of the initial conditions.

This "negative heat" would annihilate with thermal energy, but would be unable to reduce temperatures below zero or transfer to other atoms.

• I'd advise removing the science-based tag. You're already violating thermodynamics by stating that we can reach absolute zero; we can only approach it asymptotically. – HDE 226868 Aug 1 '16 at 22:17
• @HDE226868 If they want a science-based answer the tag should stay. Perhaps, as you say, the answer should be "you can't do it," but the science-based/hard-science tags should be used based on the asker's intent. – Nex Terren Aug 1 '16 at 22:19
• As to the actual question: This doesn't answer your question exactly, but has some links and is a starting-out point for Absolute Zero: physics.stackexchange.com/questions/48615/… – Nex Terren Aug 1 '16 at 22:22
• @NexTerren Yeah, but it's hard to justify using the laws of thermodynamics to answer a question when you've already broken one of them. That's my general objection to the use of the tag in this sort of situation. Plus, there are many cases where science-based + magic simply doesn't work. – HDE 226868 Aug 1 '16 at 22:22
• @HDE226868 Perhaps I should remove the question and/or add more background, then? My premise was that "temporary" heat could be added to a system, and that it would "leak out" of the observable universe over time. I was thinking it would be impossible to go below 0, so the "energy leak" would stick around and eat any energy it encountered if you added "temporary heat" and then cooled the stuff to near zero before it "leaked" back out... which raises this question. – placeholder Aug 1 '16 at 23:11

Well, let's look at the relevant part of the fundamental equation of thermodynamics: $$\mathrm dE = T\, \mathrm dS + (\text{terms irrelevant for this question})$$ Here $\delta Q = T\,\mathrm dS$ is the heat energy that goes into or out of the system. Obviously, if $T=0$, the $\delta Q=0$. In other words, you can dump entropy in it ($\mathrm dS>0$) without heating it ($\delta Q=0$).

This implies that you could use it to build a perpetual motion machine of the second kind (PM2): You extract heat ("entropic energy") from the environment, dump its entropy into the zero-temperature object, and put the energy into work.

Indeed, if you look at the Carnot efficiency, $$\eta_C = \frac{T_H - T_C}{T_H}$$ which is the maximal efficiency of a heat engine, and insert $T_C = 0$, you get $\eta_C=1$, that is, perfect efficiency, aka PM2.

However there's of course a caveat: The Carnot efficiency can only be reached for infinitely slow processes. However, there's also a formula for the efficiency at maximum power output, the Curzon-Ahlborn efficiency: $$\eta_{CA} = 1 - \sqrt{\frac{T_C}{T_H}}$$ Now if you insert $T_C=0$, you again get $\eta_{CA} = 1$. That is, with absolute zero temperature you can actually achieve an efficiency of $1$ at maximum power. That is, you can build a PM2 that actually outputs energy!

Also note that $T\,\mathrm dS=0$ also means that reversible processes cannot heat up a zero-temperature object, so it would stay at zero. Of course that equation doesn't say anything about irreversible processes (it only applies strictly to reversible ones), so an irreversible heating might still be possible.

Now if you dig deeper, I'd expect to sooner or later find some contradiction. After all, there's a reason why thermodynamics says that $T=0$ cannot be achieved.

• yeah, everything is good, but no one stated "magic" is for free. OP did not stated it's permanently 0K object, with indefinite heat capacity, or entropy capacity. That said - I do not follow your logic in answer. – MolbOrg Aug 2 '16 at 9:07
• I only applied the fundamental equations of thermodynamics (with the exception of the laws telling that absolute zero cannot be achieved, obviously). The properties of 0K objects I described follow from those laws, in the way I described. In particular, the "no (reversible-process) heating" property is not an additional assumption, but it follows from inserting $T=0$ in $\delta Q=T\,\mathrm dS$ resp. $\mathrm dE = T\,\mathrm dS + \ldots$. All I did was to insert $T=0$ in the equations and describe what the equations say in that case. – celtschk Aug 2 '16 at 9:13
• I forgot the @MolbOrg in the previous comment. – celtschk Aug 2 '16 at 9:20
• I see u point. That's true when $dS$ can be infinite small, and is continuous. There are some math restriction about when you might have differential forms of something. But on low T it is not so accurate. And one of reasons why we separate quantum mechanics. Entropy does not comes as standalone universal thing, it is derived from some assumptions in thermodynamics. Third law of thermodynamics , $\lim\limits_{T \to \, 0\, K} \left( \frac{\partial S}{\partial x} \right)_T = 0$. As you might see they do not hesitate to use 0K concept. – MolbOrg Aug 2 '16 at 10:16
• A limit $T\to 0$ is not the same as setting $T=0$. Indeed, the third law of thermodynamics says that you cannot reach $T=0$, which in turn implies that you cannot reversibly get away from $T=0$ (or else you could just reverse the process that brought you away from $T=0$ in order to reach it). – celtschk Aug 2 '16 at 10:38

I'm going to ignore my qualms that this is thermodynamically impossible, as per a reinterpretation of the third law of thermodynamics:

It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its absolute-zero value in a finite number of operations.

The entropy of a system with a temperature of absolute zero is zero; hence, no system can reach absolute zero.

Anyway, this would be the ultimate heat sink. Any matter with non-zero temperature would transfer heat to the object with a temperature of absolute zero, meaning that you could cool matter down however you wanted. Applications would include:

These would also have immense scientific applications, especially easily creating Bose-Einstein condensates.

• Those links are really cool, but don't really address what I was trying to ask; The idea is that doing this cooling is not much easier, but that there exists a method of doing marginal cooling to take the substance the rest of the way to zero. – placeholder Aug 1 '16 at 23:38
• @placeholder Ah, I didn't realize that. You might want to add that to the question. – HDE 226868 Aug 1 '16 at 23:39
• I'm not sure how to specify that in a stronger way. Should I just remove the parentheticals? – placeholder Aug 2 '16 at 1:02
• Wouldn't zero entropy imply zero kinetic energy, as in all energy would exist in potentia, as it were? The only real application would be as a paperweight. – nzaman Aug 2 '16 at 8:11
• @nzaman That's the kinetic definition of temperature, as given by the kinetic theory of gases. The thermodynamic definition states that $$T=\left(\frac{\partial U}{\partial S}\right)$$where $U$ is internal energy and $S$ is entropy. $U$ contains non-kinetic terms. This follows from the fundamental equation of thermodynamics, if we ignore the $P\mathrm{d}V$ term. – HDE 226868 Aug 2 '16 at 21:42

### A perfect cooler.

Anything made to be at 0K, permanently, would continously absorb heat from the environment.

Let the 0K-object within a room, and the room will turn into a freezer in minutes, without using an external source of energy. Unfortunately, the energy within the room is lost - that's worse than a black hole (black holes do contain energy, just hidden).

• Agreed; this is pretty much what I wrote in my answer. – HDE 226868 Aug 1 '16 at 23:34
• As noted in comments (and now specifically addressed in the question), the amount of "negative energy" is not infinite. – placeholder Aug 1 '16 at 23:35

I read an article recently in which they claimed to be able to cool a medium to one fifteen thousandth of a degree Farenheit above absolute zero. They then passed electrons through the medium which afforded them the opportunity to study the individual electrons.

I found this whole thread to be a little inane, due to the strength of the assertions being made about impossibilities, and facts about black holes, as if any one had tried hard enough to actually prove anything they were saying. Theoretical physics can be good to create theories which can be hypothesized. The problem with this branch of study arises when theories began to be widely accepted as facts despite the lack of evidence through scientific process, much like the theory of evolution. With that, I would encourage some of you to consider how little you actually know, as you may be surprised how much you can learn when you stop thinking that you already know.

Real, true, honest-to-God absolute zero would destroy modern physics. With zero temperature comes zero velocity of the particles involved, and hence zero momentum. If the particles are contained an a known volume (which seems to be implied in the question), then the Heisenburg Uncertainty principle is invalid, and from that all of quantum mechanics goes down the drain.

I think it would be the thermal equivalent of a black hole, the rate of heat transfer is proportional to the difference in temperature. It would suck the heat out of everything around it, until the whole planet was frozen.

• The intent here is that there is a finite amount of "negative energy," so freezing everything is not in the cards. – placeholder Aug 1 '16 at 22:51
• Black holes emit virtual heat – user23754 Aug 1 '16 at 22:55
• @placeholder I think you are missing my point. All heat in the area will move to whatever is being cooled, it will get harder and harder to cool off anything as it approaches absolute zero, as soon as you run out of magic particles it will heat up again. It is unlikely you will ever reach absolute zero unless you also invent a perfect insulator. – Seeds Aug 2 '16 at 18:06

It will allow very energy efficient computers, very energy efficient computations - Landauer's principle

Landauer's principle is a physical principle pertaining to the lower theoretical limit of energy consumption of computation. It holds that "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment"

trough depends how much energy needs for that "magic".