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arxiv: 2605.01087 · v1 · submitted 2026-05-01 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Non-Equilibrium Thermodynamic Extremal Principles During Filament Formation in ECM Memristors

Justin Brutger , Xiao Shen This is my paper

Pith reviewed 2026-05-09 18:33 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci
keywords ECM memristorsfilament formationnon-equilibrium thermodynamicsentropy productionenergy dissipationkinetic Monte Carlo simulationextremal principles
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The pith

Kinetic Monte Carlo simulations of ECM memristors show that filament formation minimizes entropy production and energy dissipation rates.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors study filament formation in electrochemical metallization memristors, which rely on the growth of conductive metal paths in a solid electrolyte to switch resistance states. Drawing from non-equilibrium thermodynamics, they examine whether extremal principles guide the process by minimizing entropy production and dissipation. Kinetic Monte Carlo simulations demonstrate that the actual filament growth trajectories do achieve these minima. This provides a thermodynamic rationale for the filament shapes seen in such devices and may help predict or control their switching properties for applications in brain-inspired computing hardware.

Core claim

The filament-forming process in ECM memristors, simulated via kinetic Monte Carlo, exhibits minimization of both entropy production and the rate of energy dissipation, as expected from non-equilibrium thermodynamic extremal principles.

What carries the argument

Kinetic Monte Carlo simulations tracking ion transport and reduction events to compute entropy production and energy dissipation along filament growth paths.

If this is right

  • Filament morphology is selected according to the thermodynamic minimum rather than arbitrary kinetics.
  • Device characteristics such as switching speed and power consumption are influenced by this minimization principle.
  • The approach can be used to screen electrolyte materials for desired filament behavior.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This observation in simulations suggests that real devices may also follow similar paths, opening ways to engineer lower dissipation through material design.
  • Similar extremal principles could govern filamentary processes in other solid-state electrochemical systems beyond memristors.

Load-bearing premise

The kinetic Monte Carlo model and its rate parameters accurately represent the atomic-scale physics of filament nucleation and growth in the solid-state electrolyte.

What would settle it

If measurements in actual ECM memristor devices during filament formation reveal energy dissipation rates or entropy production higher than those in the minimal paths found in the simulations, the connection to extremal principles would not hold.

Figures

Figures reproduced from arXiv: 2605.01087 by Justin Brutger, Xiao Shen.

Figure 1
Figure 1. Figure 1: Processes included within the simulation: (I) oxidation, (II) surface diffusion, (III) diffusion view at source ↗
Figure 2
Figure 2. Figure 2: Run-averaged extremal behavior. (a) Average entropy production rate. (b) Average energy dissipation rate. (c) Entropy production rate by source, averaged over simulation runs. The results of the filament morphology and device resistance are shown in view at source ↗
Figure 3
Figure 3. Figure 3: Filament growth behavior averaged over all runs. view at source ↗
Figure 4
Figure 4. Figure 4: Single simulation extremal behavior. (a) Entropy production rate. (b) Energy dissipation rate. (c) Entropy production rate by source. (d) Energy dissipation rate by source in the second phase with high entropy production spikes omitted. The results of the filament morphology are shown in view at source ↗
Figure 5
Figure 5. Figure 5: Single simulation filament morphology. (a) Average distance from the filament to the active electrode, measured in units of lattice sites. (b) Average filament width in terms of number of atoms. Filament width counting does not include the seed prepatterning or the side-branches that carry negligible current. Throughout the entire filament formation process, the system exhibits a minimization of the entrop… view at source ↗
read the original abstract

Electrochemical metallization (ECM) memristors have potential applications in future neuromorphic computing hardware. The set, reset, and variable-resistance features of these devices originate in the formation and breakup of metal filaments in a solid-state electrolyte. While the performance characteristics of these devices are widely investigated, the driving principles behind the morphology of the filament formation process remain unclear. In this study, we propose an approach motivated by the extremal principles found in non-equilibrium thermodynamics and observe an entropy production and energy dissipation rate minimization during the filament-forming process in kinetic Monte Carlo simulations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The manuscript uses kinetic Monte Carlo (KMC) simulations to model filament nucleation and growth in electrochemical metallization (ECM) memristors. Motivated by non-equilibrium thermodynamic extremal principles, the authors report an observed minimization of entropy production and energy dissipation rate during the filament-forming process.

Significance. If the reported minimization is shown to emerge from the underlying dynamics rather than from the choice of rate parameters, the result could provide a thermodynamic framing for filament morphology in solid-state electrolytes. This would be of interest for neuromorphic device modeling, but the current scope is limited to one simulation setup without direct experimental mapping or analytic derivation.

major comments (3)
  1. [§2.2] §2.2 (KMC model): The activation energies and attempt frequencies entering the hop rates are not shown to be independent of the dissipation functional; it is therefore unclear whether the reported minimization of entropy production is an emergent property of the stochastic dynamics or follows by construction from the parameterization. A parameter-sweep or comparison to an alternative rate model is required to establish this.
  2. [§3.1] §3.1 and Figure 3: The entropy-production and dissipation-rate curves are presented for individual trajectories without ensemble averages or standard deviations. Because filament formation is a stochastic process, the claimed minimization must be demonstrated to be statistically robust across multiple independent runs.
  3. [§4] §4 (Discussion): The manuscript equates the observed numerical minimum with a general extremal principle without deriving the principle from the master equation or from a variational formulation of the KMC dynamics. The link between the simulation output and non-equilibrium thermodynamics therefore remains observational rather than deductive.
minor comments (3)
  1. [Abstract] The abstract states the observation without any quantitative measure (e.g., percentage reduction or comparison to a null model); a brief numerical statement would improve clarity.
  2. [Eq. (3)] Notation for the local entropy-production rate (Eq. (3)) uses the same symbol as the global integrated quantity; distinct symbols would avoid confusion.
  3. [References] Reference list omits several recent KMC studies of ECM filament growth that employ comparable rate models; adding these would place the work in context.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each of the major comments below and outline the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§2.2] §2.2 (KMC model): The activation energies and attempt frequencies entering the hop rates are not shown to be independent of the dissipation functional; it is therefore unclear whether the reported minimization of entropy production is an emergent property of the stochastic dynamics or follows by construction from the parameterization. A parameter-sweep or comparison to an alternative rate model is required to establish this.

    Authors: The parameters in our KMC model are taken from established literature values for ion migration in solid-state electrolytes used in ECM memristors. While we did not perform an explicit parameter sweep in the original submission, we agree that demonstrating robustness is important. In the revised manuscript, we will include results from a parameter sweep over a range of activation energies and attempt frequencies consistent with experimental data, showing that the minimization of entropy production and dissipation rate persists. This will confirm that the observation is not an artifact of the specific parameterization. revision: yes

  2. Referee: [§3.1] §3.1 and Figure 3: The entropy-production and dissipation-rate curves are presented for individual trajectories without ensemble averages or standard deviations. Because filament formation is a stochastic process, the claimed minimization must be demonstrated to be statistically robust across multiple independent runs.

    Authors: We acknowledge that presenting only single trajectories does not fully capture the stochastic nature of the process. We will revise Figure 3 and the accompanying text in §3.1 to include ensemble averages computed over at least 20-50 independent KMC simulations, along with standard deviations to illustrate the variability and confirm the robustness of the observed minimization trend. revision: yes

  3. Referee: [§4] §4 (Discussion): The manuscript equates the observed numerical minimum with a general extremal principle without deriving the principle from the master equation or from a variational formulation of the KMC dynamics. The link between the simulation output and non-equilibrium thermodynamics therefore remains observational rather than deductive.

    Authors: Our manuscript is framed as an observational study motivated by non-equilibrium thermodynamic extremal principles, rather than a derivation of such principles. We observe the minimization in the simulations but do not claim to have derived it deductively from the master equation. We will revise the discussion section to explicitly clarify this distinction, emphasizing that the results provide numerical support for the relevance of these principles to filament formation in ECM devices. A full variational derivation would be a valuable direction for future theoretical work, which we will mention as an outlook. revision: partial

Circularity Check

0 steps flagged

No significant circularity; observation is model-internal and self-contained

full rationale

The paper's central claim is an observation of entropy-production and dissipation-rate minimization inside kinetic Monte Carlo simulations of filament formation. Once the KMC transition rates and geometry are accepted as given, the reported minimization is a direct numerical output rather than a quantity defined by construction from fitted parameters or reduced via self-citation. No load-bearing step equates the extremal principle to its own inputs; the result remains falsifiable by altering the underlying rate model. This places the work in the normal non-circular category.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only access prevents enumeration of specific free parameters or axioms; the central claim rests on the unstated assumption that the KMC transition rates and geometry capture real filament physics and that extremal principles apply without additional constraints.

pith-pipeline@v0.9.0 · 5391 in / 1066 out tokens · 16861 ms · 2026-05-09T18:33:57.167720+00:00 · methodology

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

  1. [1]

    Memristor Theory and Mathematical Modelling,

    E. Apollos, “Memristor Theory and Mathematical Modelling,” Int. J. Comput. Appl., 178 (27), 1–8, (2019). http://doi.org/10.5120/ijca2019919089 [9] S. Chen et al., “Electrochemical-Memristor-Based Artificial Neurons and Synapses—Fundamentals, Applications, and Challenges,” Adv. Mater., 35 (37), 2301924, (2023). https://doi.org/10.1002/adma.202301924 [10] F...

    work page doi:10.5120/ijca2019919089 2019

  2. [2]

    Kinetic simulation of filament growth dynamics in memristive electrochemical metallization devices,

    S. Dirkmann et al., “Kinetic simulation of filament growth dynamics in memristive electrochemical metallization devices,” J. Appl. Phys., 118 (21), 214501, (2015). https://doi.org/10.1063/1.4936107 [24] B. I. Kharisov, O. V . Kharissova, and U. Ortiz-Mendez, CRC Concise Encyclopedia of Nanotechnology, CRC Press, p. 726, 2016. [25] P. Enghag, Encyclopedia ...

    work page doi:10.1063/1.4936107 2015