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On the physical properties of memristive, memcapacitive and meminductive systems
Open accessAbstract
We discuss the physical properties of realistic memristive, memcapacitive and meminductive systems. In particular, by employing the well-known theory of response functions and microscopic derivations, we show that resistors, capacitors and inductors with memory emerge naturally in the response of systems-especially those of nanoscale dimensions-subjected to external perturbations. As a consequence, since memristances, memcapacitances and meminductances are simply response functions, they are not necessarily finite. This means that, unlike what has always been argued in some literature, diverging and non-crossing input-output curves of all these memory elements are physically possible in both quantum and classical regimes. For similar reasons, it is not surprising to find memcapacitances and meminductances that acquire negative values at certain times during dynamics, while the passivity criterion of memristive systems imposes always a non-negative value on the resistance at any given time. We finally show that ideal memristors, namely those whose state depends only on the charge that flows through them (or on the history of the voltage), are subject to very strict physical conditions and are unable to protect their memory state against the unavoidable fluctuations, and therefore are susceptible to a stochastic catastrophe. Similar considerations apply to ideal memcapacitors and meminductors.
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““memristors” understood merely as nonlinear resistors with memory have been described by Kubo theory in the 1950s14.”
From The Missing Memristor has Not been Found (2015) · cites this paper as [14]
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“Our perspective rests on the fact that memristive, memcapacitive, and meminductive devices and systems are simply generalizations of the traditional resistors, capacitors, and inductors to the case of memory response [6].”
From Comment on 'If it's pinched it's a memristor' (2019) · cites this paper as [6]
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BackgroundExperimental photonic quantum memristor
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“On the other hand, in [17]–[19], some significant limitations of ideal memristor models were discussed.”
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What are Memristor, Memcapacitor, and Meminductor?
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Lessons from hafnium dioxide-based ferroelectrics
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Quantum Memristors with Superconducting Circuits
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“In other words, a proper choice of the sinusoidal drive allows for tunable finite-area pinched loops [3].”
Pu, Y., Xiao, Y., & Bo, Y. (2018) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2018.2789907 · Cited by 73
“2789907 property [5]–[8] cannot enable such a memristor system to erratically change its state just under the influence of white current noise [12], [13], whose dynamic state equations allow the violation of Landauer’s principle of the minimum amount of energy [12], [14].”
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Fracmemristor: Fractional-Order Memristor
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Memristors for the Curious Outsiders
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“ing, as shown in an example taken from macroscopic granular materials [5]. In addition, hysteresis is a phenomenon that is common in nanoscale devices and it can be derived using Kubo response theory [6]. Kubo response theory is used to calculate the correction to the resistance induced by a time dependent perturbatio…”
MethodBrown, T. D., Kumar, S., & Williams, R. S. (2022) · Applied Physics Reviews · doi:10.1063/5.0070558 · Cited by 63
An Experimental Proof that Resistance‐Switching Memory Cells are not Memristors
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Self-citationInvited Article: Quantum memristors in quantum photonics
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“We have then evaluated our devices' capacity to act as memcapacitors [40], via C-V tests using multi-frequency CVU.”
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“(For example in the case of Fig.25(2a), the weaker conditionM(x) ≥ −c is sufficient for passivity of the combined system; see Appendix A.) Nonetheless, the passivity condition will be adopted in this paper, despite contrary considerations in Di Ventra and Pershin(2013).”
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Two-Dimensional Brain Microtubule Structures Behave as Memristive Devices
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“Although simple in structure, these models suffer from the innate issue that in the presence of large electric fields across the memristor, these models cannot capture the non-linear effects [11].”
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Quantum Memristors in Frequency-Entangled Optical Fields
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“Since we are assuming high-precision control of the internal variable in our system, the effect of the memristor stochastic catastrophe is negligible [30].”
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“…delays built into the dynamic response of essentially any realistic system, as predicted by the Kubo response theory [17] and conceptually detailed by Di Ventra and Per-shin specifically for memory-featuring versions of the basic circuit elements such as resistors, capacitors, and inductors [18].”
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“It has been shown in [34,99] that memristor would erratically”
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“For this application, they enable the realization of extremely energy-efficient hardware (Massimiliano and Yuriy, 2013; Ignatov et al., 2017) and have the potential of a high integration capability due to their simple two-terminal device structure (Lin et al., 2020).”
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Revisiting the memristor concept within basic circuit theory
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“The dissipative nature of the memristor was realized also by Di Ventra and Pershin,27 who point out that, as a result of such dissipative behavior, the memristor violates the time-reversal invariance.”
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“Indeed, for physical reasons [22] this is the type of elements that can mainly be realized experimentally.”
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“…by the HP group in 2008, along with those reported by other groups, is not an ideal mem-ristor but rather a memristive device defined by Chua and Kang in 1976 [67] because its memristance depends on both charge and additional state variables, rather than solely on charge [66, 70, 90 − 92] .”
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“APMs, which have practically an infinitely many numbers of states, are yet to be introduced and might even be impossible to produce due to physical limitations [12]; or it requires new quantum mechanical solutions, which are also under development [13].”
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“One of the interesting features of memristors is that these can be used both in analog or digital mode, and in combination with CMOS components [15].”
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“These theoretical foundations provide a unified device modeling approach that is (to a certain extent) compatible with the fundamental physics theories [5], such as the Kubo response theory [6].”
ResultSelf-citationCorrected and accurate Verilog-A for linear dopant drift model of memristors
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“he boundaries). These are Current-Controlled memristors: d dt w= a~i; (10) and Voltage-Controlled memristors: d dt w= b~v; (11) which are two dierent types of memristors considered in the literature [31, 32], and aand bare simply constants. In both eqns. (10) and (11) one can uses the network constraints in order to o…”
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“At the same time, the “ideal memristor” (in the sense of its original definition [3]) still remains an elusive/idealized concept, leading many researchers to raise serious concerns about its actual existence as a physically-realizable device [4, 5, 6, 7, 8].”
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“The threshold is a fundamental feature of realistic devices [23], and it is necessary for the type of operations that we want to”
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Self-citationPinched Hysteresis Loop Characteristics of a Fractional-Order HP TiO2 memristor
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Microwave quantum memcapacitor effect
Qiu, X., Kumar, S., Cárdenas-López, F. A., Barrios, G. A., Solano, E., & Albarrán-Arriagada, F. (2024) · Communications Materials · doi:10.1038/s43246-024-00505-4 · Cited by 7
“It is important to mention that our proposal differs from the ideal memory device, where the input-output relation gives perfect close loops, nevertheless, as Kubo’s response theory, these results can be linked with memory properties of the proposed device [48].”
ResultScalable oxide-based memcapacitive crossbar arrays for 1 Kb neuromorphic memory
Paul, A., Yadav, S. K., Rokade, K. A., Shembade, U. V., Hindoliya, L. K., Dubey, M., Dongale, T. D., Chueh, Y., & Mukherjee, S. (2025) · Journal of Physics D Applied Physics · doi:10.1088/1361-6463/add8a0 · Cited by 6
“V curve in capacitive-dominated systems [22].”
An experimental demonstration of the memristor test
Pershin, Y. V., Kim, J., Datta, T., & Ventra, M. D. (2022) · Physica E Low-dimensional Systems and Nanostructures · doi:10.1016/j.physe.2022.115290 · Cited by 6
“The question of whether or not the resistance switching cells are memristors [1, 2] has intrigued the scientific community since the early days of the modern ‘memristor era’ [3, 4, 5, 6, 7, 8].”
BackgroundSelf-citationGale, E., Costello, B. D. L., Erokhin, V. V., & Adamatzky, A. (2014) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2014.6865758 · Cited by 6
“The requirement that the memristor cross at the origin (as opposed to being merely pinched at the origin) was relaxed [5], [6] with suggestions that it might not be necessary condition to define a memristor [7] and that real devices can posses a ‘nanobattery’ [8].”
BackgroundMapping electric fields in real nanodevices by operando electron holography
Brodovoi, M., Gruel, K., Massebœuf, A., Chapuis, L., Hÿtch, M., Lorut, F., & Gatel, C. (2022) · Applied Physics Letters · doi:10.1063/5.0092019 · Cited by 6
ReRAM Cells in the Framework of Two‐Terminal Devices
Linn, E., Ventra, M. D., & Pershin, Y. V. (2016) · doi:10.1002/9783527680870.ch2 · Cited by 6
Self-citationNeuromorphic system using capacitor synapses
Oshio, R., Kuwahara, T., Aoki, T., Kimura, M., & Nakashima, Y. (2025) · Scientific Reports · doi:10.1038/s41598-025-87924-6 · Cited by 5
Abbasi, A., Setoudeh, F., Tavakoli, M. B., & Horri, A. (2021) · Semiconductor Science and Technology · doi:10.1088/1361-6641/abf7d4 · Cited by 5
“The memcapacitance can therefore be obtained as follows [43, 44, 47]:”
BackgroundShin, S. J., & Chung, T. D. (2021) · Chemistry - An Asian Journal · doi:10.1002/asia.202100798 · Cited by 5
Memristor, Memcapacitor, Meminductor : Models and Experimental Circuit Emulators
Kebbati, Y., Allaume, P. S., & Bennani, Y. (2022) · Engineering Technology & Applied Science Research · doi:10.48084/etasr.4882 · Cited by 4
Memristive and Memcapacitive Models of Physarum Learning
Pershin, Y. V., & Ventra, M. D. (2016) · Emergence, complexity and computation · doi:10.1007/978-3-319-26662-6_21 · Cited by 3
Self-citationHigh-Speed, Low-Power, and Area-Efficient 5T4M Memristor-Based Ternary Content Addressable Memory
Maruf, M. H., & Ali, S. I. (2023) · IETE Technical Review · doi:10.1080/02564602.2023.2279155 · Cited by 3
Low-Power Switching of Memristors Exhibiting Fractional-Order Dynamics
Astin, N., & Pershin, Y. V. (2025) · IEEE International Conference on Metrology for eXtended Reality, Artificial Intelligence and Neural Engineering (MetroXRAINE) · doi:10.1109/metroxraine66377.2025.11340470 · Cited by 2
Self-citationAn Overview of Sinusoidal Oscillators Based on Memristive Devices
Setoudeh, F., & Dezhdar, M. M. (2024) · IntechOpen eBooks · doi:10.5772/intechopen.111807 · Cited by 2
Switching synchronization in one-dimensional memristive networks: An exact solution
Slipko, V. A., & Pershin, Y. V. (2017) · Physical review. E · doi:10.1103/physreve.96.062213 · Cited by 2
Self-citationTernary Device using Graphene Memcapacitor for Post Binary Era
Patel, J. A., Sandhie, Z. T., & Chowdhury, M. H. (2018) · IEEE International Midwest Symposium on Circuits and Systems (MWSCAS) · doi:10.1109/mwscas.2018.8624098 · Cited by 2
Mahmoodpoor, A., Marunchenko, A., & Makarov, S. (2024) · Advanced Electronic Materials · doi:10.1002/aelm.202400396 · Cited by 1
Ventra, M. D., & Pershin, Y. V. (2023) · SpringerBriefs in physics · doi:10.1007/978-3-031-25625-7_2 · Cited by 1
Self-citationMulti-Level Capacitive Memory Effect in Metal/Oxide/Floating-Schottky Junction
Choi, G., Yoon, H. H., Park, K., Kim, J., Jung, S., & Chong, Y. (2019) · Journal of the Korean Physical Society · doi:10.3938/jkps.74.979 · Cited by 1
Ernoult, M. (2020) · theses.fr (ABES) · doi:10.70675/1ec5c554z9a7fz4244zaf72z8a780cac9faa · Cited by 1
Similarity between the response of memristive and memcapacitive circuits subjected to ramped voltage
Kanygin, M., Katkov, M. V., & Pershin, Y. (2017) · Journal of Nanophotonics · doi:10.1117/1.jnp.11.032507
“Energy barriers are required for nonvolatile information storage.(14,15) In the presence of barriers, the applied signal must exceed a threshold value to change the device state.”
BackgroundSelf-citationRacetrack memory based logic design for in-memory computing
Luo, T. (2018) · doi:10.32657/10356/73359
“However, the theory and related technology of the memristors are far from mature [47, 48].”
BackgroundNanostructure Biomimetic Sensing and Energy Storage: Organic Memristor/Memcapacitors
Chen, E. T. (2014) · CRC Press eBooks · doi:10.1081/e-enn3-120054061
Metadata
- Authors
- Di Ventra, M., & Pershin, Y. V.
- Affiliations
- University of South Carolina (US)
- Venue
- Nanotechnology
- Publisher
- IOP Publishing
- Published
- 2013-05-24
- Volume
- 24
- Issue
- 25
- Pages
- 255201
- ISSN
- 0957-4484 (ISSN-L)
- 1361-6528
- OpenAlex
- W2135517727
- Semantic Scholar
- c36f81401d2c03a40a32c218b3d5f1e048af075d
- Cited by
- 130
- References
- 29
- Citations by year
- 2026: 3 · 2025: 13 · 2024: 7 · 2023: 8 · 2022: 26 · 2021: 8 · 2020: 7 · 2019: 7 · 2018: 13 · 2017: 13 · 2016: 9 · 2015: 9 · 2014: 5 · 2013: 2
- FWCI
- 5.00
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Nanotechnology (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (0802830, 1202383)
- University of California, San Diego
- Division of Materials Research
- Division of Electrical, Communications and Cyber Systems (ECCS-1202383)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Memory and Neural Computing
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Ferroelectric and Negative Capacitance Devices
- Keywords
- memristors, memcapacitor, meminductor, memory elements, response functions, nanosystems, input-output curves
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