Maxwell demon may be possible after all

[Modax]

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(PhysOrg.com) -- Until now, scientists have thought that the process of erasing information requires energy. But a new study shows that, theoretically, information can be erased without using any energy at all. Instead, the cost of erasure can be paid in terms of another conserved quantity, such as spin angular momentum.

Traditionally, the process of erasing information requires a cost that is calculated in terms of energy – more specifically, heat dissipation. In 1961, Rolf Landauer argued that there was a minimum amount of energy required to erase one bit of information, i.e. to put a bit in the logical zero state. The energy required is positively related to the temperature of the system’s thermal reservoir, and can be thought of as the system’s thermodynamic entropy. As such, this entropy is considered to be a fundamental cost of erasing a bit of information.

In the study, physicists Joan Vaccaro from Griffith University in Queensland, Australia, and Stephen Barnett from the University of Strathclyde in Glasgow, UK, have quantitatively described how information can be erased without any energy, and they also explain why the result is not as contentious as it first appears. Their paper is published in a recent issue of the Proceedings of the Royal Society A.

However, Vaccaro and Barnett have shown that an energy cost can be fully avoided by using a reservoir based on something other than energy, such as spin angular momentum. Subatomic particles have spin angular momentum, a quantity that, like energy, must be conserved. Basically, instead of heat being exchanged between a qubit and thermal reservoir, discrete quanta of angular momentum are exchanged between a qubit and spin reservoir. The scientists described how repeated logic operations between the qubit’s spin and a secondary spin in the zero state eventually result in both spins reaching the logical zero state. Most importantly, the scientists showed that the cost of erasing the qubit’s memory is given in terms of the quantity defining the logic states, which in this case is spin angular momentum and not energy.

The scientists explained that experimentally realizing this scheme would be very difficult. Nevertheless, their results show that physical laws do not forbid information erasure with a zero energy cost, which is contrary to previous studies. The researchers noted that, in practice, it will be especially difficult to ensure the system’s energy degeneracy (that different spin states of the qubit and reservoir have the exact same energy level). But even if imperfect conditions cause some energy loss, there is no fundamental reason to assume that the cost will be as large as that predicted by Landauer’s formula.

The possibility of erasing information without using energy has implications for a variety of areas. One example is the paradox of Maxwell’s demon, which appears to offer a way of violating the second law of thermodynamics. By opening and closing a door to separate hot and cold molecules, the demon supposedly extracts work from the reservoir, converting all heat into useful mechanical energy. Bennett’s resolution of the paradox in 1982 argues that the demon’s memory has to be erased to complete the cycle, and the cost of erasure is at least as much as the liberated energy. However, Vaccaro and Barnett’s results suggest that the demon’s memory can be erased at no energy cost by using a different kind of reservoir, where the cost would be in terms of spin angular momentum. In this scheme, the demon can extract all the energy from a heat reservoir as useful energy at a cost of another resource.
As the scientists explained, this result doesn't contradict historical statements of the second law of thermodynamics, which are exclusively within the context of heat and thermal reservoirs and do not allow for a broader class of reservoirs. Moreover, even though the example with Maxwell’s demon suggests that mechanical work can be extracted at zero energy cost, this extraction is associated with an increase in the information-theoretic entropy of the overall system.
“The maximization of entropy subject to a constraint need apply not only to heat reservoirs and the conservation of energy,” Vaccaro explained to PhysOrg.com.
The results could also apply to hypothetical Carnot heat engines, which operate at maximum efficiency. If these engines use angular momentum reservoirs instead of thermal reservoirs, they could generate angular momentum effort instead of mechanical work.
As for demonstrating the concept of erasing information at zero energy cost, the scientists said that it would take more research and time.
“We are currently looking at an idea to perform information erasure in atomic and optical systems, but it needs much more development to see if it would actually work in practice,” Vaccaro said.
She added that the result is of fundamental significance, and it’s not likely to have practical applications for memory devices.
“We don't see this as having a direct impact in terms of practical applications, because the current energy cost of information erasure is nowhere near Landauer's theoretical bound,” she said. “It's more a case of what it says about fundamental concepts. For example, Landauer said that information is physical because it takes energy to erase it. We are saying that the reason it is physical has a broader context than that.”
More information: Joan A. Vaccaro and Stephen M. Barnett. “Information erasure without an energy cost.” Proceedings of the Royal Society A. DOI:10.1098/rspa.2010.0577

Well, even if there is no practical application in the near future, maybe someday it could result in super energy efficient quantum computers? And how awesome would it be if we can, some day, actually cheat the Second Law itself in some small way?

[Kuroneko]

Very misleading title--the point of the paper is that Maxwell's demon is impossible, but for reasons that are more general than many prior arguments supposed.

And how awesome would it be if we can, some day, actually cheat the Second Law itself in some small way?

The conclusion is the opposite, though. In quantum statistical mechanics, entropy per constituent member is given by S = -kTr(ρ.ln ρ), where the density matrix ρ is the analogue of a probability density over microstates of a canonical ensemble in classical mechanics. In thermal equilibrium, it is constant with respect to time, so the energy eigenstates diagonalize it (*), and standard thermodynamical quantities are recoverable by maximizing S subject to the constraint that the energy per constitutent member is some prescribed value (kT, if each degree of freedom is counted separately).

What Vaccaro and Barnett did [arXiv:1004.5330] is essentially the same exact thing, except instead of a reservoir exchanging energy with a heat bath, it exchanges spin with a "spin bath", with S maximized subject to the constraint that the expectation value of the number of "spin up" states in the reservoir is some prescribed value (i.e., some specific fraction of the total number of constituents). They then proceed to go through the analogous arguments as was previously done in terms of energy.

Rather than yielding some way around the second law of thermodynamics, it does opposite, providing an illustration that despite the name, the second law is more powerful than regulation of heat flow. That's something that physicists knew to some extent already (though an explicitly worked-out example is of course very nice and interesting):

The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations--then so much the worse for Maxwell's equations. If it is found to be contradicted by observation--well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

* And for finitely many microstates, it turns precisely into Shannon information entropy) scaled by k, with ρkk just being the probability pk of being in the kth eigenstate. There is an additional constraint that the probabilities sum to 1, Tr(ρ) = 1.