The unavoidable cost of computation

Here’s the pre-edited version of my latest news story for Nature. I really liked this work. I was lucky to meet Rolf Landauer before he died, and discovered him to be one of those people who is so genial, wry and unaffected that you aren’t awed by how phenomenally clever they are. He was also extremely helpful when I was preparing The Self-Made Tapestry, setting me straight on the genesis of notions about dissipative structures that sometimes assign the credit in the wrong places. Quite aside from that, it is worth making clear that this is in essence the first experimental proof of why Maxwell’s demon can’t do its stuff.
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Physicists have proved that forgetting is the undoing of Maxwell’s demon.

Forgetting always takes a little energy. A team of scientists in France and Germany has now demonstrated exactly how little.

Eric Lutz of the University of Augsburg and his colleagues have found experimental proof of a long-standing claim that erasing information can never be done for free. They present their result in Nature today [1].

In 1961, physicist Rolf Landauer argued that to reset one bit of information – say, to set a binary digit to zero regardless of whether it is initially 1 or 0 – must release at least a certain minimum amount of heat, proportional to the temperature, into the environment.

“Erasing information compresses two states into one”, explains Lutz, currently at the Free University of Berlin. “It is this compression that leads to heat dissipation.”

Landauer’s principle implies a limit on how low the energy dissipation – and thus consumption – of a computer can be. Resetting bits, or equivalent processes that erase information, are essential for operating logic circuits. In effect, these circuits can only work if they can forget – for how else could they perform a second calculation once they have done a first?

The work of Lutz and colleagues now appears to confirm that Landauer’s theory was right. “It is an elegant laboratory realization of Landauer's thought experiments”, says Charles Bennett, an information theorist at IBM Research in Yorktown Heights, New York, and Landauer’s former colleague.

“Landauer's principle has been kicked about by theorists for half a century, but to the best of my knowledge this paper describes the first experimental illustration of it”, agrees Christopher Jarzynski, a chemical physicist at the University of Maryland.

The result doesn’t just verify a practical limit on the energy requirement of computers. It also confirms the theory that safeguards one of the most cherished principles of physical science: the second law of thermodynamics.

This law states that heat will always move from hot to cold. A cup of coffee on your desk always gets cooler, never hotter. It’s equivalent to saying that entropy – the amount of disorder in the universe – always increases.

In the nineteenth century, the Scottish scientist James Clerk Maxwell proposed a scenario that seemed to violate this law. In a gas, hot molecules move faster. Maxwell imagined a microscopic intelligent being, later dubbed a demon, that would open and shut a trapdoor between two compartments to selectively trap ‘hot’ molecules in one of them and cool ones in the other, defying the tendency for heat to spread out and entropy to increase.

Landauer’s theory offered the first compelling reason why Maxwell’s demon couldn’t do its job. The demon would need to erase (‘forget’) the information it used to select the molecules after each operation, and this would release heat and increase entropy, more than counterbalancing the entropy lost by the demon’s legerdemain.

In 2010, physicists in Japan showed that information can indeed be converted to energy by selectively exploiting random thermal fluctuations, just as Maxwell’s demon uses its ‘knowledge’ of molecular motions to build up a reservoir of heat [2]. But Jarzynski points out that the work also demonstrated that selectivity requires the information about fluctuations to be stored.

He says that the experiment of Lutz and colleagues now completes the argument against using Maxwell’s demon to violate the second law, because it shows that “the eventual erasure of this stored information carries a thermodynamic penalty” – which is Landauer's principle.

To test this principle, the researchers created a simple two-state bit: a single microscopic silica particle, 2 micrometres across, held in a ‘light trap’ by a laser beam. The trap contains two ‘valleys’ where the particle can rest, one representing a 1 and the other a 0. It could jump between the two if the energy ‘hill’ separating them is not too high.

The researchers could control this height by the power of the laser. And they could ‘tilt’ the two valleys to tip the bead into one of them, resetting the bit, by moving the physical cell containing the bead slightly out of the laser’s focus.

By very accurately monitoring the position and speed of the particle during a cycle of switching and resetting the bit, they could calculate how much energy was dissipated. Landauer’s limit applies only when the resetting is done infinitely slowly; otherwise, the energy dissipation is greater.

Lutz and colleagues found that, as they used longer switching cycles, the dissipation got smaller, but that this value headed towards a plateau equal to the amount predicted by Landauer.

At present, other inefficiencies mean that computers dissipate at least a thousand times more energy per logic operation than the Landauer limit. This energy dissipation heats up the circuits, and imposes a limit on how small and densely packed they can be without melting. “Heat dissipation in computer chips is one of the major problems hindering their miniaturization”, says Lutz.

But this energy consumption is getting ever lower, and Lutz and colleagues say that it’ll be approaching the Landauer limit within the next couple of decades. Their experiment confirms that, at that point, further improvements in energy efficiency will be prohibited by the laws of physics. “Our experiment clearly shows that you cannot go below Landauer’s limit”, says Lutz. “Engineers will soon have to face that”.

Meanwhile, in fledgling quantum computers, which exploit the rules of quantum physics to achieve greater processing power, this limitation is already being confronted. “Logic processing in quantum computers already is well within
the Landauer regime, and one has to worry about Landauer's principle
all the time”, says physicist Seth Lloyd of the Massachusetts Institute of Technology.

References
1. Bérut, A. et al., Nature 483, 187-189 (2012).
2. Toyabe, S., Sagawa, T., Ueda, M., Muneyuki, E. & Sano, M. Nat. Phys. 6, 988-992 (2010).