Landauer principle

The Landauer principle is a hypothesis formulated by Rolf Landauer in 1961 which links information theory with thermodynamics and statistical physics . It states that the deletion of a bit of information inevitably releases an energy from

{\ displaystyle W = k _ {\ mathrm {B}} T \ ln 2}

in the form of warmth to the environment.

It is

${\ displaystyle k _ {\ mathrm {B}}}$ the Boltzmann constant and
${\ displaystyle T}$ the absolute temperature of the environment.

meaning

Landauer's theses are of considerable theoretical scope and form a key building block for a number of further theories, e.g. B. in basic work on quantum computers .

Reversible computers

Due to the Landauer principle, there is a theoretical lower limit for the power loss for irreversibly working computers, as almost all are today ; in practice this will be orders of magnitude higher for the time being.

This limit can only be fallen below with fundamental technical innovations such as quantum computers or reversible computers according to Charles H. Bennett . The latter are directly derived from the Landauer principle. In order to avoid deleting information, they run backwards to the initial state after the end of a calculation. To do this, all elements , from the logic gate to the programming language, must be reversibly redeveloped.

Interpretation of Maxwell's demon

Charles Bennett also proposed the interpretation of Maxwell's demon using the Landauer principle. From the above formula for the energy loss it follows immediately for the entropy released when a bit is deleted :

{\ displaystyle S = k _ {\ mathrm {B}} \ ln 2}

This entropy is released by overwriting, i.e. the implicit deletion of the demon's memory for the speed of the approaching particles. The resulting increase in entropy cancels out the decrease caused by its sorting activity.

Verification

Theoretically

Landauer's theses find positive support in the theoretical work of the American physicist Edwin Thompson Jaynes .

Criticism was expressed by the philosopher of science Orly Shenker, according to which Landauer inadmissibly mixed up the thermodynamic and the information-theoretical entropy concept.

On the theoretical level it could be shown that entanglement and quantum information can violate the Landauer principle, depending on the knowledge that an observer already has about the system.

Experimental

A first experimental confirmation of Landauer's theses was presented in March 2012 by physicists from Augsburg, Lyon and Kaiserslautern. In their experiment, a micro-glass sphere was examined in a double well potential generated by focused laser light, with 1 bit of information corresponding to the position in one well, 0 bit to the position of the sphere in the energetically deeper well.

At the quantum level, a Chinese working group was able to demonstrate the effect on a calcium atom cooled to a few microkelvins in a magnetic trap.

literature

R. Landauer: Irreversibility and Heat Generation in the Computing Process . In: IBM Journal of Research and Development . tape 5 , no. 3 , 1961, pp. 183–191 , doi : 10.1147 / around 53.0183 ( PDF ).
Rolf Landauer: The physical nature of information . In: Physics Letters A . tape 217 , no. 4-5 , 1996, pp. 188-193 , doi : 10.1016 / 0375-9601 (96) 00453-7 ( PDF ).
Charles H. Bennett: Notes on Landauer's principle, reversible computation, and Maxwell's Demon . In: Studies in History and Philosophy of Science B . tape 34 , no. 3 , 2002, p. 501-510 , doi : 10.1016 / S1355-2198 (03) 00039-X ( PDF ).

Individual evidence

↑ Orly Shenker: Logic and Entropy . 2000.
↑ Lídia del Rio, Johan Åberg, Renato Renner, Oscar Dahlsten, Vlatko Vedral: The thermodynamic meaning of negative entropy . In: Nature . tape 474 , no. 7349 , June 2, 2011, p. 61–63 , doi : 10.1038 / nature10123 .
Jump up ↑ Antoine Bérut, Artak Arakelyan, Artyom Petrosyan, Sergio Ciliberto, Raoul Dillenschneider, Eric Lutz: Experimental verification of Landauer's principle linking information and thermodynamics . In: Nature . tape 483 , no. 7388 , 2012, p. 187-189 , doi : 10.1038 / nature10872 .
↑ U. Augsburg, P. Hummel: Maxwell's demon disenchanted? , Pro Physik, March 2012.
↑ L. L. Yan, T. P. Xiong, K. Rehan, F. Zhou, D. F. Liang, L. Chen, J. Q. Zhang, W. L. Yang, Z. H. Ma, and M. Feng: Single-Atom Demonstration of the Quantum Landauer Principle , Phys. Rev. Lett. 120, 210601, doi : 10.1103 / PhysRevLett.120.210601 .
↑ Fundamental limit also applies to qubits , Spektrum.de 23 May 2018

[1] Orly Shenker: Logic and Entropy . 2000.

[2] Lídia del Rio, Johan Åberg, Renato Renner, Oscar Dahlsten, Vlatko Vedral: The thermodynamic meaning of negative entropy . In: Nature . tape 474 , no. 7349 , June 2, 2011, p. 61–63 , doi : 10.1038 / nature10123 .

[3] Jump up ↑ Antoine Bérut, Artak Arakelyan, Artyom Petrosyan, Sergio Ciliberto, Raoul Dillenschneider, Eric Lutz: Experimental verification of Landauer's principle linking information and thermodynamics . In: Nature . tape 483 , no. 7388 , 2012, p. 187-189 , doi : 10.1038 / nature10872 .

[4] U. Augsburg, P. Hummel: Maxwell's demon disenchanted? , Pro Physik, March 2012.

[5] L. L. Yan, T. P. Xiong, K. Rehan, F. Zhou, D. F. Liang, L. Chen, J. Q. Zhang, W. L. Yang, Z. H. Ma, and M. Feng: Single-Atom Demonstration of the Quantum Landauer Principle , Phys. Rev. Lett. 120, 210601, doi : 10.1103 / PhysRevLett.120.210601 .

[6] Fundamental limit also applies to qubits , Spektrum.de 23 May 2018