{"id":"5397b10f-55ae-4be1-8d88-c5b39d971de2","arxiv_id":"2506.12881","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Two interacting skyrmions at room temperature show measurable information transfer with a ~10 ms delay, non-Markovian memory from hidden trap states, and a weak but statistically significant XOR computation capability.","lead":"This paper measures how information flows between two magnetic skyrmions jiggling in a square trap at room temperature, using transfer entropy and mutual information. It finds a 10-millisecond transfer time, no Maxwell's demon in equilibrium, and a tiny but real XOR-like computation, then proposes a skyrmion-based Maxwell's demon device.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"XOR 'computational capability' lacks controls for the trivial B_n self-prediction: I(X_n; B_{n+j}) is expected to be positive even if A_n plays no role and no XOR computation occurs.","rationale":"The reader's weakest assumption focuses on binarization of continuous skyrmion positions, which is a plausible concern about preprocessing and hidden trap states. My concern is independent and more direct: even if the binarization were perfectly faithful, the XOR measurement as presented would not demonstrate computational capability because X_n includes B_n as an input and B_n is strongly autocorrelated. The nonzero MI between X_n and B_{n+j} is therefore expected from the self-prediction of B_n alone. This does not invalidate the transfer-entropy measurements or the non-Markovianity analysis, but it does undercut the 'natural computing' and 'XOR operation' claims in the abstract and main text. A control comparison is straightforward and would settle whether the effect is specific to the XOR combination. I therefore keep the reader's conditional verdict: the paper should be accepted only after this control is provided. I credit the paper for using random-number sequences as error estimates and for clearly distinguishing experimental data from model calculations of the Maxwell's demon; those parts are not the focus of this objection.","tokens_in":11259,"tokens_out":6185,"duration_ms":67026,"concrete_test":"Recompute I(X_n; B_{n+j}) (Eq. (7)) on the same binarized dataset after (i) replacing A_n with an independent balanced Bernoulli sequence and (ii) replacing A_n with a time-shuffled copy of itself. Also compute I(B_n; B_{n+j}) and I(A_n; B_{n+j}) directly for j=1-5. If the independent/shuffled controls yield the same MI as the original within statistical error, or if I(X_n; B_{n+j}) <= I(B_n; B_{n+j}) within error, the XOR computational-capability claim is not supported by the data; a positive result would require the original MI to exceed all of these controls.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central 'small but finite XOR computational capability' claim rests on a single measured quantity, I(X_n; B_{n+j}) in Eq. (7), with X_n = A_n XOR B_n. Because X_n contains B_n as one of its inputs, and the paper's own data show B_n strongly predicts its own future (I_TE^{B->B} is near 1 at j=0 and decays over tens of milliseconds), I(X_n; B_{n+j}) is expected to be positive even if skyrmion A is completely uninvolved and no XOR operation is performed. If A_n were independent of B_n with balanced marginals, I(A_n XOR B_n; B_{n+j}) would be exactly zero analytically, so a nonzero value can only reflect the A-B correlations that already exist in the thermal-equilibrium two-skyrmion system. The paper does not compare I(X_n; B_{n+j}) with I(B_n; B_{n+j}), I(A_n; B_{n+j}), or any surrogate control. Thus the claim that the system 'performs XOR computation' is not supported by the presented statistic: the positive MI may be entirely attributable to the trivial self-predictive B_n component rather than to the nonlinear XOR combination.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports an experimental study of information dynamics in a system of two magnetic skyrmions confined in a square potential well at room temperature. The authors track the Brownian motion of the skyrmions at 250 fps, binarize their x-coordinates, and compute transfer entropies and mutual informations as functions of time separation. They report a peak in transfer entropy from skyrmion A to B at about 10 ms, an attenuation time of roughly 20 ms, an absence of Maxwell's-demon-type information flow in thermal equilibrium, and evidence of non-Markovian behavior attributed to hidden trapping states. They further claim that the system exhibits a small but statistically significant 'XOR computational capability' based on the mutual information I(X_n; B_{n+j}) with X_n = A_n XOR B_n. Finally, they propose and numerically model a skyrmion-based all-solid-state Maxwell's demon operating at room temperature.","tokens_in":11443,"tokens_out":3368,"duration_ms":40096,"significance":"If the central claims are supported, the paper would be a notable experimental demonstration of information-theoretic characterization of stochastic nanomagnetic computation at room temperature, with potential implications for Brownian computing and autonomous information engines. The dataset is large (187,500 frames), and the application of transfer entropy and information thermodynamics to interacting skyrmions is timely. The paper's strengths include the direct measurement of a two-skyrmion system, the explicit check of Markovianity with additional past nodes, and the concrete proposal of a voltage-controlled Maxwell's demon. However, the significance is currently limited because the quantitative claims rest on a data-dependent binarization threshold and on an XOR statistic that lacks the necessary control comparisons.","major_comments":[{"comment":"The binarization threshold is chosen to equalize the number of 0s and 1s for each skyrmion's x-coordinate. This is a data-dependent preprocessing choice, and the paper does not demonstrate that the resulting binary series preserves the causal information structure of the continuous trajectory. Since each binary state collapses roughly 7-10 trap positions, the binary variable may be a function of the hidden trap state rather than a physical degree of freedom, and the measured transfer entropies and mutual informations could be artifacts of threshold-crossing dynamics. The authors should justify this threshold choice, e.g., by showing that the main conclusions are invariant under a range of thresholds, or by comparing the binarized results with an analysis performed directly on the continuous position series (or on a delay embedding). This is load-bearing because all quantitative claims, including the TE peak and the XOR capability, are computed from the binarized data.","section":"Section 'In order to investigate information dynamics' (binarization paragraph, near Eq. (1))"},{"comment":"The claim that the two-skyrmion system performs XOR computation is not supported without control comparisons. I(X_n; B_{n+j}) is expected to be positive even if skyrmion A plays no role, because X_n = A_n XOR B_n contains B_n as an input and the paper's own data show that B_n strongly predicts its own future (I_TE^{B->B} is near 1 at j=0 and decays over tens of milliseconds). The paper does not compare I(X_n; B_{n+j}) with I(B_n; B_{n+j}), I(A_n; B_{n+j}), or with a surrogate such as X_n computed from a time-shuffled A_n. Without such controls, the reported 0.04% mutual information cannot be attributed to the nonlinear XOR combination rather than to the trivial self-predictive component of B_n.","section":"Section 'XOR computation' and Eq. (7), Fig. 7"},{"comment":"The master-equation model is fitted to the experimental mutual information using two free parameters (epsilon_I = 0.32 kBT and R0 = 19.9 s^-1), and the residual discrepancy is then attributed post hoc to hidden information associated with trap states. This is a consistency check, not a predictive validation, and it does not independently support the claim that the observed non-Markovianity arises from hidden trap states. To make the Maxwell's demon proposal convincing, the model should be validated on a quantity not used in the fit (for example, the three-node conditional mutual informations in Fig. 5), or the fitted parameters should be compared with independently measured interaction energies and hopping rates.","section":"Section 'Model calculations' and Fig. 4(a)"},{"comment":"The open and closed 'statistical error' markers are mentioned repeatedly, but the method used to compute them is never described. It is not stated whether the errors come from bootstrap resampling, from random surrogate sequences, or from another estimator. Since the paper's significance claims depend on distinguishing signal from statistical error, this omission hampers reproducibility and should be corrected.","section":"Section 'Statistical errors' (Figs. 2, 3, 5, 7)"}],"minor_comments":[{"comment":"The notation 'j' is used for the time separation, but the text says the separation is changed from 1 to j time steps; the j=0 case for I_TE^{A->B} is excluded without explanation. Please clarify the indexing convention and how j maps to physical time.","section":"Equation (2)"},{"comment":"Two different equations are both labeled (5): the mutual information definitions and the later conditional mutual information definitions. The second should be renumbered (e.g., Eq. (6)) and subsequent equations adjusted.","section":"Equation numbering around Eq. (5) and Eq. (6)"},{"comment":"The caption states 'preventing skyrmion A from entering this location,' whereas the main text says the voltage prevents skyrmion B from entering the region. Please reconcile the discrepancy.","section":"Figure 4 caption"},{"comment":"There are numerous typos and grammatical errors, including 'extemely', 'paractical', 'Futthermore', 'equivaent', and 'paprameter'. A thorough proofreading is needed.","section":"Throughout"},{"comment":"The phrase '0.04% of maximum' is ambiguous: clarify whether this is the value of I(X_n; B_{n+j}) relative to the maximum possible mutual information of 1 bit (kB ln 2), and report the absolute value in bits as well.","section":"Abstract and XOR section"},{"comment":"The sample structure in Fig. 1(a) shows slightly different layer thicknesses from those stated in the text (e.g., Ta 0.22 nm vs 0.24 nm, CoFeB 1.2 nm vs 1.3 nm). Please ensure consistency between the text and the figure.","section":"Figure 1 and methods"}],"recommendation":"major_revision","confidential_remarks":"To the editor: This manuscript addresses an interesting and timely topic, and the experimental effort is substantial. The main concerns are the uncontrolled binarization procedure and the absent control for the XOR statistic, both of which are central to the paper's claims. These are fixable within the scope of a revision, provided the authors can supply additional analyses (threshold sensitivity, surrogate controls, and model validation against a non-fitted observable). I recommend major revision rather than rejection because the underlying phenomena (information transfer between confined skyrmions at room temperature) are likely real; however, the current presentation does not support the stronger claims of 'natural XOR computation' and a validated Maxwell's demon model."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The genuinely new thing here is the experimental measurement: transfer entropy and active information storage for two repulsively interacting skyrmions at room temperature, extracted from 187,500 frames of MOKE video. That is a real first, and the analysis is careful in the places that matter most. The paper shows a peak in A-to-B transfer entropy around 10 ms, attenuation times around 21 and 26 ms, and a finite past-future conditional mutual information that indicates non-Markovian behavior. The statistical errors are shown, and the authors openly attribute the non-Markovianity to binarization and hidden trap states. That part of the paper is solid and useful.\n\nThe soft spot is the XOR claim. They compute I(X_n; B_{n+j}) with X_n the XOR of the current binary states A_n and B_n, and take a small but significant value as evidence of nonlinear computational capability. But X_n contains B_n, and their own data show B_n predicts itself strongly at short lags. A surrogate control against I(B_n; B_{n+j}) or I(A_n; B_{n+j}) is absent. Without that, the positive mutual information may be entirely trivial self-prediction, not XOR information. The stress-test note is correct, and this needs to be fixed with proper controls before the claim is credible.\n\nTwo other issues are worth flagging, but they are more moderate. The binarization threshold is chosen to equalize counts, which is a data-dependent preprocessing step; a sensitivity analysis with different thresholds is needed to show the TE results are not an artifact. And the master equation model is fitted to the mutual information data with two free parameters, then the discrepancy is attributed to hidden information. That is post-hoc, not predictive, so the Maxwell's demon discussion should be framed as a proposal, not a demonstration.\n\nOverall, the core measurements likely survive revision, and the paper deserves a serious referee. I would send it back with a request for surrogate controls for the XOR statistic, threshold sensitivity, and a clearer separation of measured results from modeled proposals.\n\nIf I worked in skyrmion Brownian computation or experimental information thermodynamics, I would cite the transfer entropy data. For a general reading group, it is a worthwhile paper because it shows both a useful measurement and a good example of how a missing control can undermine an interpretive claim.","headline":"First room-temperature transfer entropy map of two interacting skyrmions is worth a look, but the XOR computation claim lacks the control that would make it non-trivial.","tokens_in":12061,"tokens_out":2125,"would_cite":false,"duration_ms":26149,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Two skyrmions confined in a room-temperature trap exchange measurable information, with the strongest directed flow appearing about 10 ms after the cause.","keywords":["skyrmions","transfer entropy","information thermodynamics","Maxwell's demon","Brownian computing","non-Markovianity","magnetic tunnel junction","voltage-controlled magnetic anisotropy"],"falsifier":"Re-analyze the same 187,500 frames with thresholds at other quantiles, for example 25% and 75%, or with random two-way splits, and with the full continuous positions; if the A-to-B transfer-entropy peak at about 10 ms and the XOR mutual information vanish or move outside the reported statistical errors, the central results are artifacts of the equal-count binarization rather than physical information flow.","tokens_in":10976,"feed_emoji":"🧲","tokens_out":10391,"duration_ms":108801,"temperature":0.7,"pith_summary":"Two magnetic skyrmions trapped in a square well at room temperature exchange information through their mutual repulsion, and this paper measures that exchange with information-theoretic tools. From long video recordings of Brownian motion, the authors report that directed information from skyrmion A to skyrmion B reaches a maximum about 10 ms after the cause, with an attenuation time near 21 ms, while B carries its own state forward for about 26 ms. They also find that a binary XOR of the two current positions has a small but statistically significant mutual information with B's near-future position, about 0.04% of its maximum, which they read as a primitive nonlinear computational capability in thermal equilibrium. The same data show non-Markovian behavior, which they trace to roughly 15-20 hidden trapping sites that are averaged away by binarization. A master-equation calculation then shows that equipping the two-skyrmion system with a magnetic-tunnel-junction readout and a voltage-controlled gate would produce positive information flow from A to B, making the system a built-in room-temperature Maxwell's demon.","feed_headline":"Two skyrmions swap information in 10 milliseconds","feed_subtitle":"Measured transfer entropy peaks at 10 ms; the pair also performs a tiny nonlinear XOR computation at room temperature.","key_machinery":"The analysis runs on two information-theoretic quantities. Transfer entropy reduces the future uncertainty of one skyrmion's state by knowing the other skyrmion's current state, and is computed with different time separations to locate when information arrives; a three-node variant that includes the previous node checks the Markov assumption. The subsystem time derivative of mutual information, meaning the slope of the mutual information between one skyrmion's present and the other's future, is the paper's criterion for whether one subsystem acts as a Maxwell's demon for the other. The computational test is the mutual information between $X_n = A_n \\oplus B_n$, an XOR of the two current binary states, and the future position of skyrmion B. The model calculations use a bipartite Markov jump process governed by the skyrmion interaction energy and a jump rate, with an added feedback potential step of $1 k_BT$ in the demon configuration.","core_discovery":"The central claim is that a two-skyrmion system in thermal equilibrium is a weakly information-processing device whose operation can be seen in transfer entropy. Using 250 fps video and 187,500 frames, the authors binarize each skyrmion's horizontal position at an equal-count threshold and find that the A-to-B transfer entropy rises from zero, peaks at a time separation of roughly 10 ms, and then decays with a time constant of about 21 ms; the B-to-B self-transfer entropy decays more slowly, about 26 ms. The initial slope of the mutual information between skyrmion A and future skyrmion B is zero, which in the paper's information-thermodynamics criterion means no Maxwell's-demonic feedback exists in equilibrium. A two-node analysis with an extra past node returns a finite past-to-future mutual information conditioned on the present, demonstrating that the binarized system is non-Markovian. Finally, a master-equation model with magnetic-tunnel-junction detection and voltage-controlled gating, using interaction energy 0.32 $k_BT$ and a jump rate of 19.9 s$^{-1}$, shows a positive A-to-B information flow and a negative reverse flow, which the paper interprets as a built-in Maxwell's demon that cools skyrmion A or extracts work.","pith_inferences":["If the hidden trap states are the source of non-Markovianity, then a finer readout than one bit per skyrmion, for example several bits per position or the full coordinates, should increase the measured XOR mutual information; the paper does not attempt this.","The coincidence between the 10 ms transfer-entropy peak and the skyrmion's diffusion time over its own radius suggests a general speed limit for Brownian information transfer: the propagation delay should scale roughly as distance squared divided by diffusivity, which is testable by changing skyrmion size or confinement.","Because the demon needs a measurement, the magnetic tunnel junction, and a feedback operation, voltage gating, its net energy balance depends on the cost of that measurement; the paper's entropy-flow calculation alone does not close the full power budget.","The same transfer-entropy and mutual-information diagnostics could be applied to other room-temperature Brownian tokens, such as domain walls or colloidal particles, to compare which physical systems genuinely perform nonlinear computation rather than just passing correlations."],"forward_implications":["If the analysis is right, directed information flow between two repulsively coupled Brownian skyrmions at room temperature can be measured and has a concrete timescale: about 10 ms to peak and roughly 20 ms to decay.","The nonzero past-to-future mutual information conditioned on the present means the system carries hidden memory, so hardware built from confined skyrmions should be treated as a hidden Markov system rather than a simple Markov bit.","The statistically significant XOR mutual information, though only about 0.04% of its maximum, implies that even a minimally structured two-skyrmion pair performs a nonlinear operation on its own thermal fluctuations.","The model of the feedback-controlled device predicts that the same two-skyrmion setup can act as a room-temperature Maxwell's demon, with information flow from A to B and an accompanying cooling effect on A.","Scaling skyrmions from 1.5 micrometers toward 10 nanometers would make the estimated operation speed about a nanosecond, which is the paper's stated route toward practical low-energy information engines."],"supporting_citations":[{"why":"introduces Brownian computation, the conceptual framework that motivates treating thermal skyrmion motion as a computing resource.","marker":"[2]"},{"why":"supplies the universal Brownian-circuit design with a Conservation-Join, the token-based logic the skyrmion system is meant to emulate.","marker":"[3]"},{"why":"demonstrates room-temperature Brownian motion of magnetic skyrmions, establishing the experimental regime the paper samples.","marker":"[10]"},{"why":"defines transfer entropy, the primary quantity used to measure causal information flow from skyrmion A to B.","marker":"[24]"},{"why":"provides the transfer-entropy formalism and notation used for the time-separation analysis.","marker":"[25]"},{"why":"defines information flow as the time derivative of mutual information and gives the Maxwell's-demon criterion applied to the skyrmion system.","marker":"[32]"},{"why":"identifies the mutual-information quantities used here as active information storage, grounding the two-node analysis.","marker":"[36]"},{"why":"supplies the hidden Markov model theory used to link the hidden trap states to the observed non-Markovianity and computational capability.","marker":"[37]"}],"fun_headline_variants":["Skyrmion pair shows 10ms information transfer","Two-skyrmion system does tiny XOR computation","Room-temperature Maxwell demon from two skyrmions","Non-Markovian skyrmions: info flow and a demon"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that turning each skyrmion's continuous position into a 0 or 1 at an equal-count threshold does not distort the causal relations between the two skyrmions; if the threshold and binning create the apparent correlations, the 10 ms information peak, the non-Markovianity, and the XOR signal would not describe the real physics.","fun_headline_variants_meta":{"raw":{"variants":["Skyrmion pair shows 10ms information transfer","Two-skyrmion system does tiny XOR computation","Room-temperature Maxwell demon from two skyrmions","Non-Markovian skyrmions: info flow and a demon"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000286,"raw_usage":{"total_tokens":1710,"prompt_tokens":1003,"completion_tokens":707,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":619,"completion_tokens_details":{"reasoning_tokens":641}},"tokens_in":619,"tokens_out":707,"duration_ms":9115,"temperature":1.0,"reasoning_tokens":641,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T00:36:32.404223+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-analyze the same 187,500 frames with thresholds at other quantiles, for example 25% and 75%, or with random two-way splits, and with the full continuous positions; if the A-to-B transfer-entropy peak at about 10 ms and the XOR mutual information vanish or move outside the reported statistical errors, the central results are artifacts of the equal-count binarization rather than physical information flow.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"introduces Brownian computation, the conceptual framework that motivates treating thermal skyrmion motion as a computing resource."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the universal Brownian-circuit design with a Conservation-Join, the token-based logic the skyrmion system is meant to emulate."},{"cited_title":"Schütte, J","cited_arxiv_id":null,"evidence_quote":"demonstrates room-temperature Brownian motion of magnetic skyrmions, establishing the experimental regime the paper samples."},{"cited_title":"Ishikawa, M","cited_arxiv_id":null,"evidence_quote":"defines transfer entropy, the primary quantity used to measure causal information flow from skyrmion A to B."},{"cited_title":"Schreiber, Physical Review Letters 85, 461 (2000)","cited_arxiv_id":null,"evidence_quote":"provides the transfer-entropy formalism and notation used for the time-separation analysis."},{"cited_title":"Oka and T","cited_arxiv_id":null,"evidence_quote":"defines information flow as the time derivative of mutual information and gives the Maxwell's-demon criterion applied to the skyrmion system."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"identifies the mutual-information quantities used here as active information storage, grounding the two-node analysis."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"supplies the hidden Markov model theory used to link the hidden trap states to the observed non-Markovianity and computational capability."}],"review_version":1}