Technical NotesNo Access

Memristor Equations: Incomplete Physics and Undefined Passivity/Activity

Department of Physics, San Diego State University, 5500 Campanile Drive, San Diego, CA 92182-1233, USA

School of Electrical, Computer, and Energy Engineering and Center for Solid State Electronic Research, Arizona State University, Tempe, AZ 85287-5706, USA

Search for more papers by this author

, and

Laszlo B. Kish

Department of Electrical and Computer Engineering, Texas A&M University, TAMUS 3128, College Station, TX 77843-3128, USA

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S0219477517710018Cited by:15 (Source: Crossref)

Abstract

In his seminal paper, Chua presented a fundamental physical claim by introducing the memristor, “The missing circuit element”. The memristor equations were originally supposed to represent a passive circuit element because, with active circuitry, arbitrary elements can be realized without limitations. Therefore, if the memristor equations do not guarantee that the circuit element can be realized by a passive system, the fundamental physics claims about the memristor as “missing circuit element” loses all its weight. The question of passivity/activity belongs to physics thus we incorporate thermodynamics into the study of this problem. We show that the memristor equations are physically incomplete regarding the problem of passivity/activity. As a consequence, the claim that the present memristor functions describe a passive device lead to unphysical results, such as violating the Second Law of thermodynamics, in infinitely large number of cases. The seminal memristor equations cannot introduce a new physical circuit element without making the model more physical such as providing the Fluctuation–Dissipation Theory of memristors.

Communicated by Igor Goychuk

Keywords:

References

1. L. Chua, Memristor — The missing circuit element, IEEE Trans. Circuit Theory 18 (1971) 507–519. Crossref, Web of Science, Google Scholar
2. D. B. Strukov, G. S. Snider, D. R. Stewart and R. S. Williams, The missing memristor found, Nature 453 (2008) 80–83. Crossref, Web of Science, Google Scholar
3. L. Chua, Resistance switching memories are memristors, Appl. Phys. A 102 (2011) 765–783. Crossref, Web of Science, Google Scholar
4. K. Sundqvist, D. K. Ferry and L. B. Kish, Second Law based definition of passivity/activity of devices, accepted for publication in Phys. Lett. A, doi:10.1016/j.physleta.2017.08.039; arXiv:1705.08750. Google Scholar
5. L. B. Kish, G. A. Niklasson and C. G. Granqvist, Zero-point term and quantum effects in the Johnson noise of resistors: A critical appraisal, J. Stat. Mech. 2016 (2016) 054006. Crossref, Web of Science, Google Scholar
6. L. B. Kish and T. Horvath, Notes on recent approaches concerning the Kirchhoff-Law-Johnson-Noise-based secure key exchange, Phys. Lett. A 373 (2009) 2858–2868. Crossref, Web of Science, Google Scholar
7. L. B. Kish, The Kish Cypher (World Scientific, Singapore, 2017). Link, Google Scholar
8. L. B. Kish, G. A. Niklasson and C. G. Granqvist, Zero thermal noise in resistors at zero temperature, Fluct. Noise Lett. 15 (2016) 1640001. Link, Web of Science, Google Scholar
9. L. Brillouin, Can the rectifier become a thermodynamical demon?, Phys. Rev. 78 (1950) 627–628. Crossref, Web of Science, Google Scholar
10. N. G. van Kampen, Non-linear thermal fluctuations in a diode, Physica 26 (1960) 585–604. Crossref, Google Scholar