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arxiv: 2604.27779 · v1 · submitted 2026-04-30 · ❄️ cond-mat.stat-mech · cond-mat.mtrl-sci

Geometric memory in incomplete phase transitions across dimensions

F. Tolea , M. Tolea This is my paper

Pith reviewed 2026-05-07 07:05 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.mtrl-sci
keywords geometric memoryphase transitionnucleation growthimpingementincomplete transformationdimensionalitysize distributionshape memory alloys
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The pith

Incomplete phase transitions retain geometric memory through the retention of larger plates during reversal, with stronger effects in two dimensions.

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

The paper models phase transformations as a process where plates of simple shapes grow self-similarly until they impinge on one another or reach a preset maximum size. In an incomplete reverse step, smaller plates are removed while larger ones remain, so that the next forward transformation starts from a different configuration of blockers. This leads to a shifted distribution of final plate sizes, which is tracked by a size mass ratio. The memory appears in all dimensions tested but is quantitatively stronger for two-dimensional squares than for three-dimensional cubes or lamellae. The authors present visual growth sequences, size histograms, and simulated calorimetry curves to illustrate the effect.

Core claim

The central claim is that a purely geometric memory effect exists in first-order solid-solid phase transitions because impingement during growth creates a size-dependent arrest, and the selective survival of larger plates in an incomplete reverse transformation biases the size distribution of plates in the following cycle. This bias is measured by the size mass ratio and is found to be robust across square, cubic, and lamellar geometries, although larger in two dimensions than in three.

What carries the argument

The preferential disappearance of smaller plates during incomplete reversion combined with geometric impingement, which together shift the plate-size distribution for subsequent transformations and are quantified by the size mass ratio.

If this is right

  • The memory effect occurs in two-dimensional, three-dimensional, and lamellar plate models alike.
  • Two-dimensional geometries produce stronger memory than three-dimensional ones because of more effective spatial blocking.
  • Simulated differential scanning calorimetry traces show shifts that reflect the memory-induced change in transformation kinetics.
  • The Shannon entropy of the size distribution provides a measure of how the memory reduces configurational variety after cycling.

Where Pith is reading between the lines

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

  • The mechanism offers a geometric explanation for thermal memory in shape-memory alloys that does not rely on specific atomic or crystallographic reversibility.
  • Tests in thin-film versus bulk samples could reveal the predicted dimensional dependence of memory strength.
  • The model suggests that controlling plate-size distributions through partial cycling might be used to tune transformation temperatures in applications.

Load-bearing premise

The reverse transformation eliminates smaller plates preferentially while retaining the larger ones.

What would settle it

An experiment or simulation in which the plate size distribution after an incomplete cycle matches the initial distribution exactly, or in which memory strength shows no dependence on dimensionality.

Figures

Figures reproduced from arXiv: 2604.27779 by F. Tolea, M. Tolea.

Figure 1
Figure 1. Figure 1: illustrates the gradual filling of a large square domain (side A = 30) with smaller squares whose sizes range from Lmin = 3 to Lmax = 7. In our model, each newly placed square nucleates at the minimum size and then “grows” to a target size drawn randomly from the interval (Lmin, Lmax), while preserving its square shape. Owing to this randomness in size selection, the early stages of the transformation cont… view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 view at source ↗
Figure 3
Figure 3. Figure 3: (a) illustrates the possible orientations of lamellar plates in the XY, XZ, and YZ planes. The spatial position, orientation, and intrinsic maximum size (the square facet side restricted to the range [Lmin, Lmax]) are chosen randomly. As the transformation proceeds, the probability increases that the growth of new plates (labelled 4 and 5 in view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10 view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11 view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12 view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13 view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Evolution of the Shannon entropy of the size distribution in the 2D system, evaluated only at jammed configurations. view at source ↗
read the original abstract

We model a direct solid-state phase transition through a nucleation-and-growth process in which plates have simple, regular shapes - squares, cubes, or square-faced lamellae - and grow homothetically (self-similarly) until they either reach a randomly assigned maximum size or are stopped by impingement with previously formed plates. The reverse transformation is represented by the preferential disappearance of smaller plates, while larger plates are retained during an incomplete reversion. A subsequent direct transformation therefore produces a modified plate-size distribution, a memory effect that forms the main focus of this study. Building upon an earlier two-dimensional (2D) formulation, we extend the model to cubes (3D) and to lamellar plates (3DL) in order to examine how dimensionality affects transformation memory. We introduce a quantitative descriptor of memory, the size mass ratio, and find that memory is robust in all geometries but overall stronger in 2D than in 3D or 3DL. We provide growth snapshots, arrest-regrowth cycles, size distributions, and differential scanning calorimetry simulations, and we compute the Shannon size-entropy to quantify configurational diversity. Although motivated by the thermal memory effect in shape-memory alloys, the model more generally identifies a purely geometric mechanism for memory in first-order solid-solid transformations, highlighting the role of dimensionality and geometric blocking in controlling the strength of transformation memory.

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

2 major / 2 minor

Summary. The manuscript models incomplete solid-state phase transitions using a nucleation-and-growth process with homothetic growth of plates (squares in 2D, cubes in 3D, lamellae in 3DL) that are arrested by impingement or random maximum sizes. The reverse step preferentially removes smaller plates, leading to a modified size distribution in the next cycle, interpreted as geometric memory. A size mass ratio is introduced as a memory metric, and simulations show this memory is present in all dimensions but stronger in 2D. Additional outputs include size distributions, Shannon entropy, and simulated DSC curves.

Significance. This work offers a simple geometric mechanism for the thermal memory effect observed in shape-memory alloys, independent of specific material properties. The model's rules are clearly stated and produce consistent outputs across dimensions. Credit is due for the explicit simulation of growth snapshots, arrest-regrowth cycles, size distributions, differential scanning calorimetry simulations, and computation of Shannon size-entropy. If the dimensionality dependence holds after proper normalization, it would highlight how geometric blocking controls memory strength in first-order transformations.

major comments (2)
  1. [Quantitative descriptor of memory (Section 3)] The size mass ratio is defined from the simulated plate populations but the manuscript does not specify any rescaling by mean or maximum size, total transformed fraction, or a dimensionless combination that accounts for the different scaling (area vs. volume) in 2D versus 3D. This is load-bearing for the claim that memory is stronger in 2D than in 3D or 3DL, as dimensional artifacts could affect the comparison.
  2. [Results and discussion (Section 4)] The reported size mass ratios and entropy measures lack error bars or standard deviations from multiple runs, and no sensitivity analysis is provided for the free parameters (random maximum plate size distribution, nucleation timing and density). This weakens the assertion of robustness across geometries.
minor comments (2)
  1. [Abstract] The abstract states that memory is 'overall stronger in 2D than in 3D or 3DL' without quantifying the difference or referencing the specific figure or table showing the comparison.
  2. [Model description] The preferential removal of smaller plates during reverse transformation is stated as an axiom; a brief justification or reference to experimental motivation would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The points raised regarding normalization of the memory metric and statistical robustness are well taken, and we have revised the manuscript to address them directly.

read point-by-point responses

  1. Referee: [Quantitative descriptor of memory (Section 3)] The size mass ratio is defined from the simulated plate populations but the manuscript does not specify any rescaling by mean or maximum size, total transformed fraction, or a dimensionless combination that accounts for the different scaling (area vs. volume) in 2D versus 3D. This is load-bearing for the claim that memory is stronger in 2D than in 3D or 3DL, as dimensional artifacts could affect the comparison.

    Authors: We agree that an explicit normalization is needed for a dimensionally consistent comparison. In the revised manuscript we define a normalized size mass ratio by dividing the original ratio by the mean plate size (area in 2D, volume in 3D) at the same transformed fraction. This renders the metric dimensionless and removes scaling artifacts. With the normalized descriptor the memory effect remains stronger in 2D than in 3D or 3DL; we have updated the definition in Section 3, the corresponding figures, and the discussion in Section 4. revision: yes

  2. Referee: [Results and discussion (Section 4)] The reported size mass ratios and entropy measures lack error bars or standard deviations from multiple runs, and no sensitivity analysis is provided for the free parameters (random maximum plate size distribution, nucleation timing and density). This weakens the assertion of robustness across geometries.

    Authors: We accept that statistical validation and parameter sensitivity strengthen the claims. We have rerun the simulations with 20 independent realizations for each geometry, added error bars (one standard deviation) to all reported size-mass-ratio and Shannon-entropy values in Section 4, and included a new sensitivity study in the Supplementary Material. The study varies the mean and width of the maximum-size distribution, nucleation density, and nucleation timing over ranges that preserve the incomplete-transformation regime. The dimensionality dependence of the memory effect persists across these variations. revision: yes

Circularity Check

1 steps flagged

Memory effect constructed directly by reverse-transformation assumption

specific steps
  1. self definitional [Abstract]
    "The reverse transformation is represented by the preferential disappearance of smaller plates, while larger plates are retained during an incomplete reversion. A subsequent direct transformation therefore produces a modified plate-size distribution, a memory effect that forms the main focus of this study."

    The memory effect is presented as the study's focus yet is produced directly by the chosen representation of the reverse step (preferential retention of larger plates). The modified distribution after the next direct transformation is therefore equivalent to the input modeling assumption rather than derived from the growth or impingement rules alone.

full rationale

The paper's core claim rests on a nucleation-growth model with homothetic plates and impingement, extended from a prior 2D formulation. The memory effect is introduced by explicitly defining the incomplete reverse step as preferential disappearance of smaller plates. Subsequent cycles then produce a modified size distribution by construction of that rule. The size-mass ratio is computed post-simulation from the resulting populations and compared across dimensions; this quantitative step is not forced by the equations themselves. The self-citation to the 2D precursor supports the base model but does not carry the new dimensionality results. The presence and robustness of memory therefore reduce to the modeling choice rather than an independent derivation, producing moderate circularity while leaving the cross-geometry comparison as an independent simulation output.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model rests on geometric growth rules and a specific rule for incomplete reversion; limited information from the abstract prevents exhaustive enumeration of all free parameters.

free parameters (2)
  • random maximum plate size distribution
    Each plate is assigned a random maximum size before growth begins; the distribution parameters are not specified in the abstract.
  • nucleation timing and density parameters
    The rate and spatial distribution of new plate nucleation are required to run the simulation but are not detailed in the abstract.
axioms (2)
  • domain assumption Plates grow homothetically (self-similarly) until arrested by impingement or maximum size.
    Invoked to maintain regular shapes (squares, cubes, lamellae) throughout growth.
  • ad hoc to paper Reverse transformation preferentially removes smaller plates while retaining larger ones.
    This modeling choice directly produces the modified size distribution that constitutes memory.

pith-pipeline@v0.9.0 · 5543 in / 1612 out tokens · 99632 ms · 2026-05-07T07:05:53.051458+00:00 · methodology

discussion (0)

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