From a laptop warming a knee to a supercomputer heating a room, the idea that computers generate heat is familiar to everyone. But theoretical physicists have discovered something astonishing: not only do computational processes sometimes generate no heat, under certain conditions they can even have a cooling effect. Behind this finding are fundamental considerations relating to knowledge and a lack of knowledge. The researchers publish their findings today in the journal *Nature*.

When computers compute, the energy they consume eventually ends up as heat. This isn't all due to the engineering of the computer – physics has something to say about the fundamental energy cost of processing information.

Recent research by a team of physicists reveals a surprise at this fundamental level. ETH-Professor Renato Renner, and Vlatko Vedral of the Centre for Quantum Technologies at the National University of Singapore and the University of Oxford, UK, and their colleagues describe in the scientific journal Nature how the deletion of data, under certain conditions, can create a cooling effect instead of generating heat. The cooling effect appears when the strange quantum phenomenon of entanglement is invoked. Ultimately, it may be possible to harness this effect to cool supercomputers that have their performance held back by heat generation. «Achieving the control at the quantum level that would be required to implement this in supercomputers is a huge technological challenge, but it may not be impossible. We have seen enormous progress is quantum technologies over the past 20 years,» says Vedral. With the technology in quantum physics labs today, it should be possible to do a proof of principle experiment on a few bits of data.

**Landauer's principle is given a quantum twist**

The physicist Rolf Landauer calculated back in 1961 that during the deletion of data, some release of energy in the form of heat is unavoidable. Landauer's principle implies that when a certain number of arithmetical operations per second have been exceeded, the computer will produce so much heat that the heat is impossible to dissipate. In supercomputers today other sources of heat are more significant, but Renner thinks that the critical threshold where Landauer's erasure heat becomes important may be reached within the next 10 to 20 years. The heat emission from the deletion of a ten terabyte hard-drive amounts in principle to less than a millionth of a joule. However, if such a deletion process were repeated many times per second then the heat would accumulate correspondingly.

The new study revisits Landauer's principle for cases when the values of the bits to be deleted may be known. When the memory content is known, it should be possible to delete the bits in such a manner that it is theoretically possible to re-create them. It has previously been shown that such reversible deletion would generate no heat. In the new paper, the researchers go a step further. They show that when the bits to be deleted are quantum-mechanically entangled with the state of an observer, then the observer could even withdraw heat from the system while deleting the bits. Entanglement links the observer's state to that of the computer in such a way that they know more about the memory than is possible in classical physics.

**Similar formulas – two disciplines**

In order to reach this result, the scientists combined ideas from information theory and thermodynamics about a concept known as entropy. Entropy appears differently in these two disciplines, which are, to a large extent, independent of each other. In information theory, entropy is a measurement of the information density. It describes, for instance, how much memory capacity a given set of data would take up when compressed optimally. In thermodynamics, on the other hand, entropy relates to the disorder in systems, for example to the arrangement of molecules in a gas. In thermodynamics, adding entropy to a system is usually equivalent to adding energy as heat.

The ETH physicist Renner says «We have now shown that in both cases, the term entropy is actually describing the same thing even in the quantum mechanical regime». As the formulas for the two entropies look the same, it had already been assumed that there was a connection between them. «Our study shows that in both cases, entropy is considered to be a type of lack of knowledge», says Renner. The new paper in Nature builds on work published earlier in the *New Journal of Physics*.

In measuring entropy, one should bear in mind that an object does not have a certain amount of entropy per se, instead an object's entropy is always dependent on the observer. Applied to the example of deleting data, this means that if two individuals delete data in a memory and one has more knowledge of this data, she perceives the memory to have lower entropy and can then delete the memory using less energy. Entropy in quantum physics has the unusual property of sometimes being negative when calculated from the information theory point of view. Perfect classical knowledge of a system means the observer perceives it to have zero entropy. This corresponds to the memory of the observer and that of the system being perfectly correlated, as much as allowed in classical physics. Entanglement gives the observer „more than complete knowledge" because quantum correlations are stronger than classical correlations. This leads to an entropy less than zero. Until now, theoretical physicists had used this negative entropy in calculations without understanding what it might mean in thermodynamic terms or experimentally.

**No heat, even a cooling effect**

In the case of perfect classical knowledge of a computer memory (zero entropy), deletion of the data requires in theory no energy at all. The researchers prove that "more than complete knowledge" from quantum entanglement with the memory (negative entropy) leads to deletion of the data being accompanied by removal of heat from the computer and its release as usable energy. This is the physical meaning of negative entropy.

Renner emphasizes, however, "This doesn't mean that we can develop a perpetual motion machine". The data can only be deleted once, so there is no possibility to continue to generate energy. The process also destroys the entanglement, and it would take an input of energy to reset the system to its starting state. The equations are consistent with what's known as the second law of thermodynamics: the idea that the entropy of the universe can never decrease. Vedral says "We're working on the edge of the second law. If you go any further, you will break it."

**Fundamental findings**

The scientists' new findings relating to entropy in thermodynamics and information theory may have usefulness beyond calculating the heat production of computers. For example, methods developed within information theory to handle entropy could lead to innovations in thermodynamics. The connection made between the two concepts of entropy is fundamental.

**Explore further:**
Could Maxwell's Demon Exist in Nanoscale Systems?

**More information:**
Del Rio L, Aberg J, Renner R, Dahlsten O & Vedral V: The thermodynamic meaning of negative entropy, *Nature* (2011) DOI:10.1038/nature10123

## chardo137

## TabulaMentis

"The equations are consistent with what's known as the second law of thermodynamics: the idea that the entropy of the universe can never decrease. Vedral says "We're working on the edge of the second law. If you go any further, you will break it."

Maybe we will have a new thermodynamic law in the coming years?

## hemitite

## CSharpner

I was thinking the same thing, but I don't think so... kind of depends on how you define "time" too. Suppose you had a theoretical machine that allowed you to step outside of space time and then manipulate every subatomic particle in the universe and place it back to the way it was at some point in the past, with all the quantum effects, then set it in motion, and then step back into the regular space-time of the universe. Suppose, according to your own watch, it took you trillions of trillions of years to set it to that state. When you're done, did you /actually/ go back in time? Does it matter? Practically, no, it doesn't matter. but, theoretically? I don't know.

It seems that at the quantum level, time is much less of a definitive property.

## ECOnservative

## Mahal_Kita

Actually no. You would not go back in time, you would create an alternate reality. Stepping back, as you put it, would take the same effort.

## MorituriMax

Forget Asimov, check out the entry for "Cryo-arithmetic engines" here: http://en.wikiped...on_Space

Neat.

## hush1

You see? QM/Information Theory all makes sense now.

I apologize for Erwin. He meant well.

This is not some antics of semantics like Armit's suggesting spacetime without time.

## antonima

## hush1

http://en.wikiped...ectivity

## hush1

http://www.math.c...0g/noll/

## Foolish1

Excuse me for being naive and foolish but this sure sounds like nonsensical double talk to me.

Computers don't often 'erase' memory they replace the contents.

If you erase something without actually removing the information is this really a physically useful property? Sooner or later you must either run out of memory or 'erase' previous information and pay the (deferred) tax then.

## TomSullivan

The entropy of true space is extremely low, (near-zero). Entropy is very low, or "near-zero", in true space because the only form entropy can take within true space is the form of gravity fluctuations, vacuum fluctuations, or "quantum fluctuations". Upon the initiation of true space ripping, entropy would rise a very small amount. The "pure energy" that forms at the initiation of ripping would have extremely low entropy. Each one-dimensional rip that forms would have "perfect" symmetry within itself. The two edges of a single rip would be of equal length, and of opposite energy, the two edges of each individual rip would be "equal and opposite". As separation occurs between the edges of these rips, symmetry is broken and entropy increases dramatically. (As areas of true space form within these rips, the gravity that each edge of each rip experiences becomes very asymmetric and the edge collisions that occur cause the two edges of each individual rip to become greatly uneven, thus greatly increasing their entropy. The result of this is "broken symmetry" and "large entropy".)

As the rips adjust to this new entropy, the degree of entropy somewhat stabilizes. Over time the entropy of each "proximity" within the universe changes, but the overall entropy of the universe remains somewhat stable. Sooner or later many of these rips will approach black holes. As each rip comes to the event horizon of a black hole, the energy in each of it's edges' that is "equal and opposite" will "combine" and collapse, thus becoming true space once again. But the uneven energy in those two edges, the energy that is not exactly "equal and opposite" (not "symmetrical"), remains as a very small rip with very uneven edges. At this point, the surface of the even horizon would be at maximum entropy. (As previously predicted.) The energy that remains in each rip would consist of only the "uneven energies" that are left in the two edges of that rip. (The two edges of each remnant of rip would be highly asymmetrical.) With only "uneven energy" left in each edge of a single rip, the rips that "define the surface of the even horizon" are at maximum entropy. (Rip Theory predicts that the rips "directly adjacent" to a black hole define that black hole, they define the perimeter of the black hole, they define the "event horizon's surface".) Since the rip edges only contain uneven energy at this point, entropy would be at 100%, (or "near-100%"). These rips with "totally uneven energies" in their edges are accelerated away from the "surface of the event horizon" by the collapse of the "equal but opposite" energy they had contained. They are accelerated outward by the "matter-antimatter" reaction that occurs due to the equal but opposite energies within the edges "annihilating" each other and "collapsing". Within the black hole entropy is very low, since Rip Theory considers black holes to be true space, their entropy would be limited to the gravity fluctuations, vacuum fluctuations, and quantum fluctuations that occur in true space.

© Copyright 2011 Thomas A. Sullivan

## codeslingerMalthius

## hush1

That space X is contractible if and only if the identity map from X to itselfwhich is always a homotopy equivalenceis null-homotopic. Your constants are showing. (Blush)

The "no prior geometry" demand remains unfulfilled.

The adage, 'the map is not the territory', remains.

:)

## LordOfTheNerds