Landauer's principle

Landauer's principle

Landauer's Principle, first argued in 1961ref|landauer by Rolf Landauer of IBM, holds that "any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information bearing degrees of freedom of the information processing apparatus or its environment". (Bennett 2003)ref|bennett.

Specifically, each bit of lost information will lead to the release of an amount "kT ln 2" of heat, where "k" is the Boltzmann constant and "T" is the absolute temperature of the circuit. On the other hand, if no information is erased, computation may in principle be achieved which is thermodynamically reversible, and require no release of heat. This has led to considerable interest in the study of reversible computing.

The principle is widely accepted as "physical lore"; but in recent years it has been challenged, notably in Earman and Norton (1998), and subsequently in Shenker (2000)ref|shenker and Norton (2004)ref|norton, and then defended by Bennett (2003)ref|bennett and Short et al. (2007).ref|short


Landauer's principle can be understood to be a simple logical consequence of the second law of thermodynamics—which states that the entropy of a closed system cannot decrease—together with the definition of thermodynamic temperature. For, if the number of possible logical states of a computation were to decrease as the computation proceeded forward (logical irreversibility), this would constitute a forbidden decrease of entropy, unless the number of possible physical states corresponding to each logical state were to simultaneously increase by at least a compensating amount, so that the total number of possible physical states was no smaller than originally (total entropy has not decreased).

Yet an increase in the number of physical states corresponding to each logical state means that for an observer who is keeping track of the logical state of the system but not the physical state (for example an "observer" consisting of the computer itself), the number of possible physical states has increased; in other words, entropy has increased from the point of view of this observer. The maximum entropy of a bounded physical system is finite. (If the holographic principle is correct, then physical systems with finite surface area have a finite maximum entropy; but regardless of the truth of the holographic principle, quantum field theory dictates that the entropy of systems with finite radius and energy is finite.) So, to avoid reaching this maximum over the course of an extended computation, entropy must eventually be expelled to an outside environment at some given temperature "T", requiring that energy "E" = "ST" must be emitted into that environment if the amount of added entropy is "S". For a computational operation in which 1 bit of logical information is lost, the amount of entropy generated is at least "k" ln 2, and so the energy that must eventually be emitted to the environment is "E" ≥ "kT" ln 2.

This expression for the minimum energy dissipation from a logically irreversible binary operation was first suggested by John von Neumann, but it was first rigorously justified (and with important limits to its applicability stated) by Landauer. For this reason, it is sometimes referred to as being simply the "Landauer bound" or "limit."


* Rolf Landauer, " [ Irreversibility and heat generation in the computing process] ," IBM Journal of Research and Development, vol. 5, pp. 183-191, 1961.
* [ Notes on Landauer's principle, Reversible Computation and Maxwell's Demon] by Charles H. Bennett. Studies in History and Philosophy of Modern Physics vol. 34 pp. 501-510 (2003).
* [ Logic and Entropy] Critique by Orly Shenker (2000)
* [ Eaters of the Lotus] Critique by John Norton (2004)
* [ The Connection between Logical and Thermodynamic Irreversibility] Defense by Short et al. (2007)

External links

* [ Introductory article on Landauer's principle and reversible computing]

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Landauer — is a surname, and may refer to:* Bernhard Landauer * Gustav Landauer, German anarchist, writer, and critic * M. H. Landauer, Writer on Jewish mysticism; born in 1808 at Kappel * Rolf Landauer, German American physicist; born in 1927 at Stuttgart… …   Wikipedia

  • Landauer-Prinzip — Das Landauer Prinzip ist eine Hypothese und besagt, dass das Löschen eines Bits an Information zwangsläufig die Abgabe einer Energie von in Form von Wärme an die Umgebung bedeutet. T ist dabei die absolute Temperatur der Umgebung, k die Boltzmann …   Deutsch Wikipedia

  • Landauer, Rolf William — ▪ 2000       German born American physicist whose discovery of what came to be known as Landauer s principle that the erasing of computer information causes a loss of energy led to the development of more efficient computers (b. Feb. 4, 1927,… …   Universalium

  • Rolf Landauer — Infobox Scientist name = Rolf Landauer caption = Rolf William Landauer birth date = February 4, 1927 birth place = Stuttgart, Germany residence = U.S. nationality = American death date = April 27, 1999 death place = Briarcliff Manor, New York,… …   Wikipedia

  • Entropy in thermodynamics and information theory — There are close parallels between the mathematical expressions for the thermodynamic entropy, usually denoted by S , of a physical system in the statistical thermodynamics established by Ludwig Boltzmann and J. Willard Gibbs in the 1870s; and the …   Wikipedia

  • Reversible computing — is a model of computing where the computational process to some extent is reversible, i.e., time invertible. A necessary condition for reversibility of a computational model is that the transition function mapping states to their successors at a… …   Wikipedia

  • Maxwell's demon — In the philosophy of thermal and statistical physics, Maxwell s demon is a thought experiment created by the Scottish physicist James Clerk Maxwell to show that the Second Law of Thermodynamics has only a statistical certainty. [1] It… …   Wikipedia

  • CBH-Theorem — Das CBH Theorem ist eine informationstheoretische Rekonstruktion der Quantenmechanik, die 2003 von den Philosophen R. Clifton, J. Bub und H. Halvorson ausgearbeitet wurde. Der Name des Theorems geht auf die Initialen seiner Autoren zurück. Gemäß… …   Deutsch Wikipedia

  • MASORAH — This article is arranged according to the following outline: 1. THE TRANSMISSION OF THE BIBLE 1.1. THE SOFERIM 1.2. WRITTEN TRANSMISSION 1.2.1. Methods of Writing THE ORDER OF THE BOOKS SEDARIM AND PARASHIYYOT …   Encyclopedia of Judaism

  • History of anarchism — Part of the Politics series on Anarchism …   Wikipedia