What is Information?

Matter, energy… knowledge: How to harness physics' demonic power

By Stephen Battersby

Published by New Scientist Magazine 14^th May 2016   Subscribe here

Running a brain-twisting thought experiment for real shows that information is a physical thing – so can we now harness the most elusive entity in the cosmos?

WE LIVE in the age of information. We are surrounded by it, and more of it year by year. It is the currency of human understanding, our indispensable guide to navigating a complex world. But what, actually, is information?

As we have wrestled with the question over the years, we have slowly begun to realise it is more than an abstraction, the intangible concept embodying anything that can be expressed in strings of 1s and 0s. Information is a real, physical thing that seems to play a part in everything from how machines work to how living creatures function.

Recently came the most startling demonstration yet: a tiny machine powered purely by information, which chilled metal through the power of its knowledge. This seemingly magical device could put us on the road to new, more efficient nanoscale machines, a better understanding of the workings of life, and a more complete picture of perhaps our most fundamental theory of the physical world.

For at its heart, information is a mystery bound up with thermodynamics. This set of iron rules explains how heat is converted to and from other forms of energy, and governs a huge variety of processes. Thermodynamics makes a vital distinction between heat – a melee of random motions of atoms and molecules – and work, energy directed towards a purpose, such as the action of an engine pushing a car along.

Perhaps the most cast-iron of the thermodynamic rules is the second law, which says that heat will not flow from a cool object to a warmer one unless you put in some work. Otherwise we could exploit this heat flow to do work and produce a perpetual motion machine.

But is it so cut and dried? The idea that there could be exceptions to the second law dates from 1867, when James Clerk Maxwell concocted a thought experiment. He imagined a "very intelligent and exceedingly quick" entity able to see the motions of air molecules. Given a box of hot air and another of cold air connected by a frictionless door, it could use this knowledge alone to allow fast moving molecules to pass one way and slower ones the other, making the hot box hotter and the cold box colder. Heat would flow without work being done – a brazen violation of the second law (see diagram).

This being soon came to be known as Maxwell's demon, an apt name because it presents us with a hellish problem. Thermodynamics is a monumentally robust theory, surviving intact even after many ideas were swept aside by quantum theory and relativity in the 20th century. Yet the demon demands an explanation thermodynamics can't supply. Something was missing.

A clue to what that might be came when physicist Leo Szilard imagined a pared-down version of the demon in 1929. In this scenario, a single molecule is trapped in a box, and the demon can see which end the molecule is in at any given moment. The demon slides a partition into the middle of the box and lets the bouncing molecule push it up to one end, against a little resistance. That means it is doing work. The demon's knowledge amounts to one bit of information, equivalent to a 0 or 1, and Szilard worked out how much work the demon can extract with its one bit. At room temperature it turns out to be about 3 x 10^-21joules of work, or enough to lift a bacterium about a nanometre. It was a hint that information might be the missing piece of thermodynamics.

Others realised that the demon's trick depends on its knowledge of the molecules but Szilard's breakthrough was to quantify the information the demon needed. In 1961, Rolf Landauer, a researcher at IBM in New York, took things further, showing that erasing a computer's memory requires work. His colleague Charles Bennett applied this result to the demon, reasoning its knowledge must be stored in some sort of finite memory that would sooner or later have to be erased for it to keep running. He calculated that the demon would have to expend at least as much work on this task as can be gained from the boxes of gas it is meddling with.

Accounting for the cost of deleting information restored some balance to the demon's thermodynamic world, but it was a little unsatisfactory. The demon still gets away with bending the second law for a while – until its head gets too full.

And there our understanding stuck, until a flurry of new insights emerged over the past decade. A crucial result came in 2008, from Takahiro Sagawa and Masahito Ueda at the Tokyo Institute of Technology. They worked out that you can salvage the second law by adding an extra term called mutual information (Physical Review Letters, vol 100, p 080403). This is a measure of how much the demon knows about whatever system it is looking at. "You can think of the measurement as a correlation between the system and an apparatus or memory," says Juan Parrondo, who studies the thermodynamics of information at the Complutense University of Madrid, Spain.

Sagawa and Ueda's updated second law shows how much work you can extract from a system for a given amount of demonic knowledge. It doesn't hold only when memory is erased. "You can apply it to more general situations," says Parrondo. "The consequences are quite peculiar."

One consequence is that blank memory can be a kind of fuel, an idea described in 2012 by Chris Jarzynski and Dibyendu Mandal at the University of Maryland, College Park. If Maxwell's demon receives new empty memory, it can write information to it and do useful work as a consequence – Jarzynski and Mandal's example is lifting a weight. That blank memory could simply be a paper tape bearing a long string of zeros, although to do anything meaningful you would need a lot of them: 300 billion billion zeros allow the demon to lift an apple by 1 metre.

Such a bizarre idea demands proper testing. And that meant summoning a real demon, a feat that's proved difficult. Maxwell's original thought experiment involved a demon with a complex mind, with inner depths that are impossible to fathom. That is no good for a physics experiment. In 2010, Shoichi Toyabe then as at Chuo University in Tokyo and his colleagues built a working demon using a tinyplastic rotor, a camera and a computer. This was a step away from human-like intelligence, but it still involved large-scale paraphernalia, so it was impossible to show exactly what was happening inside the demon. Better would be a very small and simple demon – really more of an imp – in which the flows of heat, work and information could be clearly traced.

That's just what was conjured up in Finland last year. Jukka Pekola and his team at Aalto University in Espoo created a microscopic demon of chilling and powerful simplicity. Their set-up, originally suggested by Massimiliano Esposito at the University of Luxembourg and his colleagues, is based on two quantum dots, devices that can briefly trap single electrons. One is known as the system, the other is the demon. The demon usually holds an electron, loosely. When an electron reaches the system, it repels and ejects the demon's electron electrostatically. This process robs the system electron of some potential energy, which means that when it leaves the quantum dot it must use up some of its thermal energy to do so. The result is that it arrives in the wires cooler than when it left (see diagram).

Once unleashed, this unholy set-up works fast. Within a second millions of chilled electrons arrive in the wires, reducing their temperature by about one-thousandth of a kelvin. Meanwhile, the demon's temperature rises. "It is challenging to get everything to work," says Pekola. "But as soon as the demon is tuned to the right position you don't have to do anything: it is autonomous."

Crucially, the demon electron is on such a hair trigger that the electrostatic repulsion forcing it to leave is doing essentially no work, certainly not enough to lower the other electron's energy by the extent seen.

With no work being done, how can the system cool while the demon gets hotter? The feat seems impossible until we incorporate Sagawa and Ueda's mutual information. Pekola's team have shown that the cooling works exactly as predicted if mutual information is balancing the books. "It is exchanging information that results in a change in temperature," says Sebastian Deffner at the Los Alamos National Laboratory in New Mexico.

Energy catalyst

If information alone can have a physical effect, then it is a physical thing. So what kind of thing is it? There are two ways of looking at it. One is to consider information as a form of entropy, the quantity in thermodynamics that expresses disorder. In Maxwell's thought experiment, that equates to how mixed up the molecules are. The more disordered they are, the more information the demon must have to do its job.

Another way to think of information is as a kind of energy catalyst: it enables you to convert the chaotic energy of heat to the useful energy of work. So when people say information is power, they're not far wrong.

Yet this is hardly the last word on the nature of information. For one thing, although Pekola's demon involves single electrons, they are constrained to behave mostly like classical particles that don't exhibit the strangest features of the quantum world.

Quantum particles can show superposition, being in two places simultaneously. And two or more particles can be entangled, correlated with one another in such a way that measuring one affects the properties of the other. "In quantum systems the situation is much more complicated," says Deffner. "Some energy and some information is encoded in the correlations but we have to better understand where to put this in the equations."

Pekola plans to create a truly quantum demon, one that operates on qubits, the quantum mechanical equivalent of a bit, which can be both 0 and 1 simultaneously. The most likely option is to make one out of a superconducting electronic circuit, which would emit a single photon when it changes state. To peer into the mind of the quantum demon he will need a new type of single-photon detector, which several teams around the world are working towards.

But now we're arming ourselves with a firmer understanding of information, what does it all mean? Well, Pekola's demon is not going to bring us perpetual motion. It is still governed by the restrictions Landauer hit upon: it can create a temperature difference that could be used to do work, but only at the cost of repeatedly wiping its memory, which requires work.

But demons can still perform special tasks for us. "They could be useful to move heat somewhere that is not so critical in your circuit," says Pekola. In other words, demons could act as local refrigerators in nanoelectronics, especially important for the powerful quantum computers of the future.

Meet your demon

These ideas could also have implications for our understanding of biology. "Organisms sensing their environment have to expend energy, with fundamental limitations based on information," says Jordan Horowitz at the Massachusetts Institute of Technology. And according to the mutual-information tweak of the second law, acquiring information requires a minimum energy outlay.

By studying how E. coli bacteria sense the concentration of certain chemicals, Horowitz and his colleagues worked out that they use only about twice the theoretical minimum. So maybe the fundamental cost of processing information is a significant burden cells have had to learn to cope with.

Like bacteria, humans are on one level information-processing machines, so did the fundamental cost of information processing shape us? Parrondo has analysed the proofreading process in DNA transcription, where enzymes pause, go back and cut out erroneously placed base pairs. He concluded that this activity is designed to optimise a three-way trade-off between speed, accuracy and energy use. The situation is more complex than Maxwell's demon, and the maths he used is different. So it's not yet clear whether the fundamental energy requirements of processing information really have affected the evolution of error-checking. "We would like to have the same framework for all types of problem. We don't have it yet," says Parrondo.

Some even think there may be demons within us. Kinesins are motor proteins that clamber around our cells, transporting other proteins and whatnot. According to Martin Bier at East Carolina University in Greenville, North Carolina, kinesins may use a form of position-sensing feedback, akin to Maxwell's demon, to move more efficiently. Parrondo is not convinced, however. "This is very speculative," he says.

There's more to learn about the role demons might play inside us or the computer minds of the future. But one of their kind has already opened the door of knowledge, just a crack, to reveal a glimpse of information's true nature.

This article appeared in print under the headline "The unseen agent"

Stephen Battersby is a consultant for New Scientist