Landauer's Principle

IN 1961 Rolf Landauer (1927-1999) applied thermodynamic reasoning to digital computers, providing a bridge between information theory and physics. There are many publications regarding this subject. Here I just want to present, according to [2], a simple and quick way to state Landauer’s principle, regarding classical (non-quantum) information in classical systems.

In his original paper [1] Landauer had the important insight that there is a fundamental asymmetry in the way Nature allows us to process information. Copying classical information can be done reversibly and without wasting any energy, but when information is erased there is always an energy cost of kT ln2 per classical bit to be paid. For example, as shown in fig. 1, we can encode one bit of information in a binary device composed of a box with a partition.
Fig1 We erase the information of the position of the atom. First we extract the wall separating the two halves of the box. Then we use a piston to shift the atom to the left side of the box. After the procedure, the atom is on the lefthand side of the box irrespective of its intial state. Note that the procedure has to work irrespective of whether the atom is initially on the right (a) or on the left side (b).

The box is filled with a one molecule gas that can be on either side of the partition, but we do not know which one. We assume that we erase the bit of information encoded in the position of the molecule by extracting the partition and compressing the molecule in the right part of the box irrespective of where it was before. We say that information has been erased during the compression because we will never find out where the molecule was originally. Any binary message encoded is lost! The physical result of the compression is a decrease in the thermodynamical entropy of the gas by kln2. The minimum work that we need to do on the box is kT ln2, if the compression is isothermal and quasi-static. Furthermore an amount of heat equal to kT ln2 is dumped in the environment at the end of the process. Landauer’s conjectured that this energy/entropy cost cannot be reduced below this limit irrespective of how the information is encoded and subsequently erased – it is a fundamental limit.

It can be shown that Landauer’s principle can be deduced from the second law of thermodynamics and is in fact equivalent to it [3]. Earman and Norton have argued that since it is not independent of the Second Law, it is either unnecessary or insufficient as an exorcism of Maxwell’s Demon. A response to this objection was given by Bennet [5].

In practice, almost all data processing is done on macroscopic apparatus, dissipating macroscopic amounts of energy far in excess of what would be required by Landauer’s principle. Nevertheless, some stages of biomolecular information processing, such as transcription of DNA to RNA, appear to be accomplished by chemical reactions that are is reversible not only in principle but in practice.

[1] R. Landauer, Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, (1961) pp.183-191 [pdf].

[2] M. B. Plenio and V. Vitelli, The physics of forgetting: Landauer’s erasure principle and information theory, arXiv:quant-ph/0103108 v1 19 Mar 2001.

[3] B. Schumacher, Relative entropy in quantum information theory, arXiv:quant ph/0004045 10 Apr 2000.

[4] John Earman and J. D Norton, "Exorcist XIV: The Wrath of Maxwell's Demon." Studies in the History and Philosophy of Modern Physics, Part I "From Maxwell to Szilard" 29(1998), pp.435-471; Part II: "From Szilard to Landauer and Beyond," 30(1999), pp.1-40. Download Part I Download Part II.

[5] Charles H. Bennet, Notes on Landauer’s Principle, Reversible Computation, and Maxwell Demon, Studies in History and Philosophy of Modern Physics, 34, (2004) pp. 501-510, arXiv : physics/0210005 v2 9 Jan 2003.