1. bookVolume 117 (2020): Issue 1 (January 2020)
Journal Details
License
Format
Journal
eISSN
2353-737X
First Published
20 May 2020
Publication timeframe
1 time per year
Languages
English
access type Open Access

An Explanation of the Landauer bound and its ineffectiveness with regard to multivalued logic

Published Online: 28 Dec 2020
Volume & Issue: Volume 117 (2020) - Issue 1 (January 2020)
Page range: -
Received: 13 Oct 2020
Accepted: 18 Nov 2020
Journal Details
License
Format
Journal
eISSN
2353-737X
First Published
20 May 2020
Publication timeframe
1 time per year
Languages
English
Abstract

We discuss, using recent results on the thermodynamics of multivalued logic, the difficulties and pitfalls of how to apply the Landauer’s principle to thermodynamic computer memory models. The presentation is based on Szilard’s version of Maxwell’s demon experiment and use of equilibrium Thermodynamics. Different versions of thermodynamic/mechanical memory are presented – a one-hot encoding version and an implementation based on a reversed Szilard’s experiment. The relationship of the Landauer’s principle to the Galois connection is explained in detail.

Keywords

Bennett, C.H. (1973). The logical reversibility of computation. IBM Journal of Research and Development, 17, 525–532.10.1147/rd.176.0525Search in Google Scholar

Bennett, C.H. (1987). Demons, Engines and the Second Law. Scientific American, 257.10.1038/scientificamerican1187-108Search in Google Scholar

Bérut, A. at al. (2012). Experimental verification of Landauer’s principle linking information and thermodynamics. Nature, 483, 187–189. http://doi.org/10.1038/nature1087210.1038/nature1087222398556Search in Google Scholar

Bormashenko, E. (2019). Generalization of the Landauer Principle for Computing Devices Based on Many-Valued Logic. Entropy, 21(12), 1150. http://doi.org/10.3390/e2112115010.3390/e21121150Search in Google Scholar

Bormashenko, E. (2019). The Landauer Principle: Re-Formulation of the Second Thermodynamics Law or a Step to Great Unification?. Entropy, 21(10), 918. https://doi.org/10.3390/e2110091810.3390/e21100918Search in Google Scholar

Fong, B., Spivak, D.I. (2019). An Invitation to Applied Category Theory: Seven Sketches in Compositionality. Cambridge University Press.10.1017/9781108668804Search in Google Scholar

Frankel, T. (2011). Geometry of Physics. Cambridge University Press.10.1017/CBO9781139061377Search in Google Scholar

Hayes, B. (2001). Third base. American Scientist, 89, 490–494.10.1511/2001.40.3268Search in Google Scholar

Kycia, R.A. (2018). Landauer’s Principle as a Special Case of Galois Connection. Entropy, 20(12), 971. https://doi.org/10.3390/e2012097110.3390/e20120971751257133266695Search in Google Scholar

Kycia, R.A. (2020). Entropy in Themodynamics: from Foliation to Categorization, Accepted to Communications in Mathematics; arXiv:1908.07583 [math-ph].Search in Google Scholar

Ladyman, J., Presnell, S., Short, A.J., Groisman, B. (2007). The connection between logical and thermodynamic irreversibility. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 38, 1, 58–79. https://doi.org/10.1016/j.shpsb.2006.03.00710.1016/j.shpsb.2006.03.007Search in Google Scholar

Landauer, R. (1961). Irreversibility and heat generation in the computing process. IBM Journal of Research and Development, 5, 183–191.10.1147/rd.53.0183Search in Google Scholar

Parrondo, J.M.R., Horowitz, J.M., Sagawa, T. (2015). Thermodynamics of information. Nature Phys, 11, 131–139. https://doi.org/10.1038/nphys323010.1038/nphys3230Search in Google Scholar

Piechocinska, B. (2000). Information erasure. Phys. Rev. A, 61, 062314. https://doi.org/10.1103/PhysRevA.61.06231410.1103/PhysRevA.61.062314Search in Google Scholar

Raschka, S., Mirjalili, V. (2017). Python Machine Learning. Birmingham: Packt Publishing.Search in Google Scholar

Reza, F.M. (1994). An Introduction to Information Theory, Dover Publications.Search in Google Scholar

Sagawa, T. (2014). Thermodynamic and logical reversibilities revisited. Journal of Statistical Mechanics: Theory and Experiment, P03025, 3. http://doi.org/10.1088/17425468/2014/03/p03025Search in Google Scholar

Smith, P., Category Theory: A Gentle Introduction, Retrieved from https://www.logicmatters.net/categories (date of access: 10/10/2020).Search in Google Scholar

Still, S. (2019). Thermodynamic cost and benefit of data representations. Phys. Rev. Lett. (in press); arXiv:1705.00612Search in Google Scholar

Szilard, L. (1929). Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen (On the reduction of entropy in a thermodynamic system by the intervention of intelligent beings). Zeitschrift für Physik, 53, 840–856. http://doi.org/10.1007/BF01341281 (English translation: NASA document TT F-16723).10.1007/BF01341281Search in Google Scholar

Yan, L.L., Xiong, T.P., Rehan, K., Zhou, F., Liang, D.F., Chen, L., Zhang, J.Q., Yang, W.L., Ma, Z.H., Feng, M. (2018). Single-Atom Demonstration of the Quantum Landauer Principle. Phys. Rev. Lett., 120, 210601. https://doi.org/10.1103/PhysRevLett.120.21060110.1103/PhysRevLett.120.21060129883174Search in Google Scholar

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