Maxwell's fridge

I haven’t generally been putting up here the pieces I’ve been writing for Physical Review Focus, as they can tend to be a bit technical. But as I’ve been writing this and that about Maxwell’s demon elsewhere, I thought I’d post this one. The final version is here.

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In 1867 the physicist James Clerk Maxwell described a thought experiment in which the random thermal fluctuations of molecules might be rectified by intelligent manipulation, building up heat that might be used to do useful work. Now in Physical Review Letters a team at the University of Maryland outline a theoretical scheme by which Maxwell’s nimble-fingered ‘demon’ might be constructed in an autonomous device that in effect uses computation to transfer heat from a cold substance to a hotter one, thereby acting as a refrigerator.

Maxwell believed that his demon might oppose the second law of thermodynamics, which stipulates that the entropy of a closed system must always increase in any process of change. Because this law seems to be statistical – an entropy increase, or increase in disorder, is simply the far more likely outcome – the demon might undermine it, for example by physically reversing the usual scrambling of hot and cold molecules and thereby preventing the diffusion of heat.

Most physicists now agree that such a demon wouldn’t defeat the second law, because of an argument developed in the 1960s by Rolf Landauer [1]. He showed that the cogitation needed to perform the selection would have a compensating entropic cost – specifically, the act of resetting the demon’s memory dissipates a certain minimal amount of heat per bit erased.

Despite this understanding, there have been few attempts to postulate an actual physical device that might act as a Maxwell demon. Last year, Christopher Jarzynski and Dibyendu Mandal at Maryland proposed such a ‘minimal model’ of an autonomous device [2]. It consisted of a three-state device (the ‘demon’) that can extract energy from a reservoir of heat and use it to do useful work. The transitions in the demon are linked the writing of bits into a memory register – a tape recording binary information – which moves past the it, according to particular coupling rules.

In collaboration with their colleague Haitao Quan, now at Peking University, Mandal and Jarzynski have now refined their model so that the demon is a two-state device coupled to heat exchange between a hot and a cold reservoir. Again, the operation of the demon is ensured by the coupling rules imposed between its transitions, the reservoirs and the memory, resulting in a mathematically solvable model whose performance depends on the model’s parameters.

The demon can absorb heat from the hot reservoir to reach its excited state, and reverse that process, without altering the memory. But the rules say that energy may only be exchanged with the cold reservoir by coupling to the memory. The demon can absorb heat from the cold reservoir if the incoming bit is a 0, or release it if the bit is a 1. And whenever energy is exchanged with the cold reservoir, the demon reverses the bit, which affects the entropy of the outgoing bit stream. So each 0 allows the chance for energy to move from the cold reservoir into the demon – and potentially then out to the hot reservoir.

The researchers find that the behaviour of the system depends on the temperature gradient and the relative proportions of 1s and 0s in the incoming bit stream. In one range of parameters the device acts as a refrigerator, drawing heat from the cold reservoir colder while imprinting a memory of this operation as 1s in the outgoing bit stream. In another range it acts as an information eraser: lowering the excess of 0s in the bit stream and thus randomizing this ‘information’, while allowing heat transfer from hot to cold.

Jarzynski says that, while the model couples heat flow and information, it doesn’t have Landauer’s condition explicitly built in. Rather, this condition emerges from the dynamics, and so the results provide some support for Landauer’s interpretation.

How might one actually build such a system? “We don’t have a specific physical implementation in mind”, Jarzynski admits, but adds that “we are exploring a fully mechanistic Rube Goldberg-like contraption where the demon and memory are represented by wheels and paddles that rotate about the same axis and interact by bumping into one another.”

Trying to figure out how a physical device might act like Maxwell’s demon is “an important task”, according to Franco Nori of the University of Michigan. “To build such a system in the future would be another story, but this is a very important step in the right direction,” he says.

Although he sees this as “an interesting theoretical model of Maxwell's demon”, Charles Bennett of IBM’s research laboratory in Yorktown Heights, New York, thinks it could be made even simpler. “It’s somewhat unrealistic and unnecessarily complicated to have the tape move at a constant velocity”, he says – the parameter describing the tape speed could be eliminated “by coupling each 0→1 tape transition to a forward step of the tape and each 1→0 transition to a backward step.”

References
1. R. Landauer, IBM J. Res. Dev. 5, 183 (1961).
2. D. Mandal & C. Jarzynski, Proc. Natl Acad. Sci. USA 109, 11641-11645 (2012).