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

  • 1 Faculty of Materials Science and Physics, Cracow University of Technology
  • 2 University of Warmia and Mazury, Faculty of Mathematics and Computer Science

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.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • Bennett, C.H. (1973). The logical reversibility of computation. IBM Journal of Research and Development, 17, 525–532.

  • Bennett, C.H. (1987). Demons, Engines and the Second Law. Scientific American, 257.

  • Bérut, A. at al. (2012). Experimental verification of Landauer’s principle linking information and thermodynamics. Nature, 483, 187–189. http://doi.org/10.1038/nature10872

  • 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/e21121150

  • 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/e21100918

  • Fong, B., Spivak, D.I. (2019). An Invitation to Applied Category Theory: Seven Sketches in Compositionality. Cambridge University Press.

  • Frankel, T. (2011). Geometry of Physics. Cambridge University Press.

  • Hayes, B. (2001). Third base. American Scientist, 89, 490–494.

  • Kycia, R.A. (2018). Landauer’s Principle as a Special Case of Galois Connection. Entropy, 20(12), 971. https://doi.org/10.3390/e20120971

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

  • 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.2006.03.007

  • Landauer, R. (1961). Irreversibility and heat generation in the computing process. IBM Journal of Research and Development, 5, 183–191.

  • Parrondo, J.M.R., Horowitz, J.M., Sagawa, T. (2015). Thermodynamics of information. Nature Phys, 11, 131–139. https://doi.org/10.1038/nphys3230

  • Piechocinska, B. (2000). Information erasure. Phys. Rev. A, 61, 062314. https://doi.org/10.1103/PhysRevA.61.062314

  • Raschka, S., Mirjalili, V. (2017). Python Machine Learning. Birmingham: Packt Publishing.

  • Reza, F.M. (1994). An Introduction to Information Theory, Dover Publications.

  • 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/p03025

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

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

  • 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).

  • 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.120.210601

OPEN ACCESS

Journal + Issues

Search