## Landauer's Principle

*27 Feb 2017 16:30*

A (somewhat disputed) result in statistical mechanics, linking it to computation and information theory, named after Rolf Landauer. (In a shocking violation of Stigler's Law of Eponym, Landauer really does seem to have been the first to articulate it.) The principle is that erasing one bit of information must produce at least \( kT \ln 2 \) joules of heat, where \( T \) is the absolute temperature and \( k \) is Boltzmann's constant. This is held to be because erasing one bit must increase entropy by one bit, i.e., by \( \ln 2 \) nats, and since heat is related to entropy (by \( dS = dQ / T \), erasure must produce heat.

For a long time, I thought that this was both an obviously correct and a very deep argument, but reading some critical papers by Shenker and Norton in 2005 persuaded me that the argument above is much too hasty, and that other arguments were at least doubtful if not invalid. I have remained in a state of doubt, suspended judgment, and curiosity ever since.

- Recommended:
- David Albert, Time and Chance [For the discussions of Maxwellian and pseudo-Maxwellian demons]
- John Earman and John Norton, "Exorcist XIV: The wrath of
Maxwell's Demon"
- "From Maxwell to Szilard", Studies in the
History and Philosophy of Modern Physics
**29**(1998): 435--471 - "From Szilard to Landauer and beyond", Studies in
the History and Philosophy of Modern Physics
**30**(1999): 1--40

- "From Maxwell to Szilard", Studies in the
History and Philosophy of Modern Physics
- Owen Maroney, "Information Processing and Thermodynamic Entropy", Stanford Encyclopedia of Philosophy
- John D. Norton
- "Eaters of the Lotus: Landauer's Principle and the Return of Maxwell's Demon", phil-sci 1729
- "The End of the Thermodynamics of Computation: A No-Go Result", Philosophy of Science
**80**(2013): 1182--1192 [See also. --- Actually, I think an important caveat is in order here. Norton's math shows that every phase in the reversible computation has to be equi-probable, but then he leaps from that to asserting that the phases have to appear*in random order*. To see that this is invalid, observe that position of a clock is equi-probable over time, but they follow in a strict (and computationally useful) sequence.] - "Waiting for Landauer", phil-sci/8635

- Orly Shenker, "Logic and Entropy", phil-sci 115 [Claims Landauer's principle is wrong]
- W. H. Zurek (ed.), Complexity, Entropy, and the Physics of Information

- To read:
- A. E. Allahverdyan and Th. M. Nieuwenhuizen, "Breakdown of the Landauer bound for information erasure in the quantum regime," cond-mat/0012284 [Color me skeptical]
- A. C. Barato, D Hartich, U. Seifert, "Information-theoretic vs. thermodynamic entropy production in autonomous sensory networks",
Physical Review E
**87**(2013): 042104, arxiv:1212.3186 - M. Maissam Barkeshli, "Dissipationless Information Erasure and the Breakdown of Landauer's Principle", cond-mat/0504323
- Charles H. Bennett, "Notes on Landauer's principle, reversible
computation, and Maxwell's Demon", Studies In History and Philosophy of
Science Part B
**34**(2003): 501--510 - Antoine Bérut, Artak Arakelyan, Artyom Petrosyan, Sergio Ciliberto, Raoul Dillenschneider and Eric Lutz, "Experimental verification of Landauer's principle linking information and thermodynamics",
Nature
**483**(2012): 187--189 [While I am impressed by the delicacy of the experiment, there seems to be a huge logical gap between "*we*couldn't do any better in this system" and "it is*impossible*to do any better with this system", let alone "it is*impossible*to do any better with*any*system". But I should read the paper carefully before condemning it.] - A. Daffertshofer and A. R. Plastino, "Landauer's principle and the
conservation of information", Physics Letters
A
**342**(2005): 213--216 - Raoul Dillenschneider and Eric Lutz, "Memory Erasure in Small Systems", Physical
Review Letters
**102**(2009): 210601 - Léo Granger, Holger Kantz, "Differential Landauer's principle", arxiv:1302.6478
- Rolf Landauer, "The Physical Nature of Information,"
Physics Letters A
**217**(1996): 188--193 - Dibyendu Mandal, H. T. Quan, and Christopher Jarzynski, "Maxwellâ€™s Refrigerator: An Exactly Solvable Model", Physical Review Letters
**111**(2013): 030602 - O. J. E. Maroney
- "The (absence of a) relationship between thermodynamic and logical reversibility", arxiv:0406137
- "Generalising Landauer's Principle", Physical
Review E
**79**(2009): 031105, arxiv:quant-ph/0702094

- Takahiro Sagawa and Masahito Ueda
- "Jarzynski Equality with Maxwell's Demon", cond-mat/0609085
- "Minimal Energy Cost for Thermodynamic Information Processing: Measurement and Information Erasure",
Physical
Review Letters
**102**(2009): 250602, arxiv:0809.4098

- Tony Short, James Ladyman, Berry Groisman and Stuart Presnell, "The Connection between Logical and Thermodynamical Irreversibility", phil-sci 2374
- Aaron Sidney Wright, "The Physics of Forgetting: Thermodynamics of Information at IBM 1959--1982", Perspectives on Science
**24**(2016): 112--141