{"id":"8f5ee1be-9246-4f5b-87fd-07287948b739","arxiv_id":"2607.14795","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Explicitly sampling atomic identity arrangements in alchemical thermodynamic integration lowers the predicted AuCu order-disorder transition from ~818 K to ~721 K and yields full phase diagrams for three DFT functionals.","lead":"The authors present a computer workflow that builds an alloy phase diagram by explicitly sampling atomic vibrations and the many arrangements of atoms on the lattice, then apply it to gold-copper. It matters because they show that including real atomic arrangements shifts the predicted AuCu ordering temperature by about 100 K—but that a bigger uncertainty comes from the underlying electronic-structure approximation.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Analytic ideal-mixing term in Eqs. (4)–(5) may double-count the combinatorial entropy already sampled by identity-exchange moves; no partition-function derivation is given, and the SGC benchmark (reported as both 700 K and 1000 K) is a single-temperature check.","rationale":"The central claim is that explicit configurational sampling lowers the AuCu order–disorder Tc by ~97 K and changes phase-field widths. This claim rests on absolute free-energy differences between phases; a composition- or temperature-dependent error of the size of the ideal-mixing term would change these differences by tens of meV and shift Tc by hundreds of K. The reader's weakest-assumption pinpoints exactly this risk: Eqs. (4)–(5) add an analytic ideal-mixing term to a path whose λ=0 state, with identity-exchange moves active, already enumerates all N!/(N_A!N_B!) label assignments. The paper provides no partition-function derivation for the combined MC/MD ensemble, so the cancellation (if any) between the sampled combinatorial entropy and the analytic term is not shown. I independently checked the algebra: if the λ=0 partition function includes the full sum over assignments, then the analytic term exactly cancels that factor and Eq. (5) recovers the physical mixing free energy. So the bookkeeping may be correct; the problem is that the paper does not demonstrate it, and the one benchmark that could catch a residual error is weakened by an internal inconsistency (700 K vs 1000 K) and by sharing the same swap implementation. A non-interacting U=0 test would settle the issue unambiguously because the correct answer is known analytically. I therefore agree with the reader's conditional verdict: the paper is plausible and promising, but should not be fully accepted until the partition-function bookkeeping is either derived or verified by this zero-interaction check (and the benchmark temperature is corrected).","tokens_in":19893,"tokens_out":30238,"duration_ms":263521,"concrete_test":"Zero-interaction consistency test: set U_A = U_AB = 0 (or U_AB = U_A) and run the full alchemical protocol with identity-exchange moves for several compositions x and temperatures T (e.g., 300, 700, 1000 K). The total free-energy difference F(T,x) − F(T,0) from Eq. (5) must equal the analytic ideal-mixing plus de Broglie terms exactly, with no residual nswap dependence, because the excess free energy is zero. If the result deviates from kBTN[x ln x + (1−x)ln(1−x)] (+ de Broglie) by more than statistical error, or changes with nswap, the combinatorial factor is mis-bookkept and the AuCu phase boundaries in Fig. 5 cannot be considered quantitative. This test isolates the bookkeeping question from potential/model errors and would settle the double-counting concern directly.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The weakest point is the free-energy bookkeeping in §4.1–4.2. Eq. (5) adds the analytic ideal-mixing term kBTN[(1−x)ln(1−x)+x ln x] on top of an alchemical work integral whose λ=0 endpoint already carries N!/[(xN)!((1−x)N)!] identity assignments sampled by Metropolis exchange moves (§4.2.2, Algorithm 1). No equation in the paper derives the partition function of the combined MD/MC sampler, so it is not established whether the combinatorial factor is canceled by the analytic term or counted twice. If it is double-counted, the error is composition-dependent and linear in T, reaching ~60 meV/atom near x=0.5 at 1000 K—far larger than the 1 meV/atom precision that the paper itself says shifts Tc by ~30 K. The SGC-MC/MD comparison is not a complete safeguard: it is performed at one temperature, the manuscript inconsistently reports that temperature as 700 K (main text, §2.2) and 1000 K (Supplementary Note 2, Fig. 3), and the two methods share the same identity-swap implementation, so a common bookkeeping bias would not be exposed. A composition-dependent bookkeeping error would directly corrupt the free-energy surfaces used to build Fig. 5 and the reported 97 K shift, which is the paper's central quantitative result.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a workflow that extends non-equilibrium thermodynamic integration to composition-dependent alchemical transformations, combining Monte Carlo identity-exchange moves with molecular dynamics so that configurational and vibrational entropy are sampled in a single free-energy calculation. The method is applied to Au–Cu using ACE potentials trained on LDA, PBE, and r2SCAN DFT data. Free energies are computed for the FCC solid solution, ordered intermetallics, and the liquid, and phase diagrams are assembled through a semi-grand-canonical Legendre transformation. For the ACE-LDA potential, explicit configurational sampling lowers the AuCu order–disorder transition temperature from about 818 K to 721 K (closer to the experimental 683 K) and substantially widens the solid-solution field, while the dependence on the exchange-correlation functional is much larger. The authors are careful to caution that the agreement with experiment should not be overinterpreted.","tokens_in":20290,"tokens_out":17456,"duration_ms":181760,"significance":"If the methodology is correct, it offers a direct, general route from machine-learned interatomic potentials to binary phase diagrams that include non-ideal configurational entropy and fully anharmonic vibrational entropy without empirical thermodynamic fitting. The paper has notable strengths: parameter-convergence tests in Fig. 2, validation of the ACE potentials against DFT convex hulls (Fig. 1), a comparison with semi-grand canonical MC/MD, consistency with an independent EAM nested-sampling result, and openly available training data, potentials, and codes. The candid discussion of functional sensitivity is also a strength. However, the central free-energy bookkeeping — specifically the relation between the analytic ideal-mixing term and the identity-exchange sampling — is not derived at the partition-function level, and the benchmark used to support the bookkeeping is reported at inconsistent temperatures. These points must be resolved before the quantitative claims can be accepted.","major_comments":[{"comment":"The paper does not provide a partition-function-level derivation showing that the analytic ideal-mixing term in Eq. (4) is not already included in the combined MD/MC sampling. At λ=0 the potential is independent of σ, so the identity-exchange moves visit all N!/(NA!NB!) assignments; at λ=1 they sample the equilibrium distribution over σ. The relationship between the sampled partition function and the terms in Eq. (4) should be written out explicitly, including the indistinguishability prefactors and the combinatorial degeneracy, to demonstrate the cancellation that justifies adding kBTN[(1−x)ln(1−x)+x ln x]. Without this, a reader cannot rule out a composition-dependent double counting of the ideal-mixing entropy, which would directly affect the reported 97 K shift and the phase fields in Fig. 5.","section":"§4.1–4.2, Eqs. (4)–(5), Algorithm 1"},{"comment":"The benchmark against SGC-MC/MD is presented at inconsistent temperatures: the main text states the comparison is made at 700 K, while Supplementary Note 2 and Fig. 3 state 1000 K, and the convergence figures in the SI are captioned 700 K. The temperature matters because the solid solution is not stable across the full composition range at all temperatures. Moreover, this benchmark is performed at a single temperature, and both methods share the same identity-swap implementation, so a common bias in the energy evaluation or in the treatment of identity labels would not be exposed. The authors should reconcile the reported temperature and, ideally, add a second temperature or provide an explicit argument why one temperature is sufficient to validate the composition-dependent bookkeeping.","section":"§2.2 and Supplementary Note 2"},{"comment":"The 'no-swap' or 'ideal-mixing' baseline uses a fixed random identity assignment rather than an ensemble average over assignments. At λ=1 in the no-swap calculation, the free energy corresponds to one particular configuration of the species plus the analytic ideal-mixing term; it is not the free energy of the ideal-mixing ensemble, which would require averaging the enthalpy over all assignments. It should be clarified how many independent random assignments were used, how the 818 K baseline and the 97 K shift depend on the chosen assignment, and what the associated uncertainty is. As written, the comparison between 'with' and 'without' configurational sampling may conflate the absence of configurational entropy with the absence of configurational enthalpy relaxation.","section":"§2.3, Fig. 3; §4.2.2"}],"minor_comments":[{"comment":"The abstract states the transition is lowered from approximately 810 K to 710 K, while §2.3 reports 818 K to 721 K. The numbers should be made consistent.","section":"Abstract vs §2.3"},{"comment":"The main text says a 1 meV/atom free-energy difference can cause 'more than 50 K' change in transition temperature, whereas Supplementary Note 4 estimates ±29 K for the order–disorder transition. These should be reconciled.","section":"§2.2 vs Supplementary Note 4"},{"comment":"The text of the note says the SGC-MC/MD comparison is at 1000 K, while the captions of Supplementary Figs. 1 and 2 say 700 K. This inconsistency must be fixed.","section":"Supplementary Note 2"},{"comment":"Typographical issues: 'Finaly' in §2.5, 'less then 1.8 Å' in §4.5.1, and a missing article in §4.5.2 ('The exact location of the cross-over point...').","section":"General"},{"comment":"The repositories listed in Refs. [50] and [51] are appropriate, but the version identifiers should be cited consistently so that the exact datasets and potentials used in the paper can be retrieved.","section":"§5 / Data and code availability"}],"recommendation":"major_revision","confidential_remarks":"The central idea is timely and the application is well executed, but the lack of a partition-function derivation for the ideal-mixing bookkeeping is the kind of issue that a careful reader will not be able to resolve from the text alone. The 700 K/1000 K inconsistency in the benchmark is a red flag that needs to be cleaned up before the quantitative claims can be trusted. I believe the issues are fixable within the scope of a revision, hence major_revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe headline: this is a serious methods paper with a new-seeming combination—alchemical NE-TI with MC identity-exchange moves—that produces full binary phase diagrams from ACE potentials, and it's mostly convincing. The AuCu demonstration is thorough: convergence checks on swap counts, switching time, and MD relaxation; three XC functionals; validation against DFT hulls; a comparison with an EAM potential that matches nested sampling; and well-documented fits. The main result, a ~97 K lowering of the AuCu order-disorder Tc from configurational sampling, is plausible, and the authors are appropriately cautious about the functional dependence.\n\nWhat's new: the combination of composition-dependent alchemical interpolation with Metropolis identity swaps in an automated workflow (calphy/landau) is something I don't think anyone has done end-to-end. The introduction correctly situates it against prior work (Li & Scandolo, etc.). The phase diagrams are genuinely predictive in the sense that nothing is tuned to the experimental 683 K.\n\nThe soft spots. The biggest one is the bookkeeping in Eqs. (4)–(5). You add an analytic ideal-mixing term to a path whose endpoints both carry the same combinatorial factor from identity-exchange sampling. No derivation shows that the work integral excludes that factor. If it doesn't, you're double-counting a composition-dependent entropy, which at 1000 K would be tens of meV/atom—far larger than the 1 meV/atom precision the paper itself says shifts Tc by ~30 K. The SGC-MC/MD agreement to ~3.7 meV/atom is reassuring, but the two methods share the same swap implementation, and the benchmark is at one temperature, so it doesn't fully rule out a common bookkeeping bias. This needs a partition-function derivation or an independent numerical test—e.g., a lattice model with a known answer.\n\nMinor: the SGC benchmark temperature is reported as 700 K in §2.2 and 1000 K in Suppl. Note 2/Fig. 3. That's a typo or worse, and it should be corrected. Also, the treatment of the ordered phase as defect-free is an acknowledged approximation; fine.\n\nThere are no invented entities, the potentials and data are posted, and the self-citations (calphy, landau, ASSYST) are prior, independently published tools. The circularity is low; they explicitly caution against overinterpreting agreement with experiment.\n\nWho is this for? Anyone working on atomistic phase diagram prediction from MLIPs, especially in alloys where configurational entropy matters. It earns a serious referee slot, but the referee should push for the derivation.\n\nRecommendation: send to peer review, conditional on the authors deriving the partition function for the combined MD/MC sampler and resolving the SGC temperature inconsistency. If the derivation reveals a double-count, the 97 K shift is compromised; if it's clean, this is a nice step forward.","headline":"A promising alchemical NE-TI + identity-exchange workflow with honest benchmarking, but the free-energy bookkeeping is under-derived and needs proof before the 97 K shift can be trusted.","tokens_in":20769,"tokens_out":14836,"would_cite":true,"duration_ms":127219,"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":"By sampling atomic identity swaps on top of alchemical thermodynamic integration, the authors compute Au-Cu phase diagrams directly from atomistic free energies and show that explicit configurational entropy lowers the order-disorder transi","keywords":["binary phase diagrams","configurational entropy","vibrational entropy","nonequilibrium thermodynamic integration","alchemical transformation","identity-exchange Monte Carlo","Au-Cu alloy","atomic cluster expansion"],"falsifier":"Recompute the alchemical transformation at xCu=0.5 and 1000 K with the analytic ideal-mixing term removed from the free-energy formula. If the resulting free energy differs from the published value by k_B T ln2 per atom (about 0.060 eV/atom at 1000 K), the term was double-counted; if it agrees, the bookkeeping is consistent.","tokens_in":19795,"feed_emoji":"🧪","tokens_out":5026,"duration_ms":47733,"temperature":0.7,"pith_summary":"The paper extends non-equilibrium thermodynamic integration so that a single atomistic free-energy calculation captures both atomic vibrations and the distribution of chemical species over sites. It does this by alchemically interpolating one element into another while Monte Carlo identity-exchange moves reshuffle species identities along the switching path. Applied to Au-Cu with ACE potentials trained on three DFT functionals, the method produces full composition-temperature phase diagrams directly from atomistic free energies. Explicit configurational sampling lowers the predicted AuCu order-disorder transition by about 97 K, from 818 K to 721 K, bringing it close to the experimental 683 K, and markedly widens the solid-solution and solubility fields. The same comparison shows functional choice shifts transition temperatures by hundreds of kelvin, so configurational entropy and functional accuracy must both be handled explicitly.","feed_headline":"Configurational entropy shifts AuCu ordering by 97 K","feed_subtitle":"Alloy phase diagrams sampled with explicit identity swaps put the predicted order-disorder transition at 721 K, near the measured 683 K.","key_machinery":"The load-bearing mechanism is alchemical non-equilibrium thermodynamic integration: a linear interpolation H(λ)=(1−λ)H_i+λH_f switches a subset of atoms from pure-A to A-B interactions over a finite switching time, and the bidirectional work average gives ΔF. To sample configurational entropy, Metropolis identity-exchange moves swap the species labels of one A and one B atom between MD blocks along the path (Algorithm 1), so that at each λ the simulation equilibrates over both atomic positions and identity assignments in the interacting system. The composition dependence is completed by adding analytic ideal-mixing and de Broglie terms; phase diagrams follow from Legendre-transforming F(T,x)","core_discovery":"The paper's central claim is that vibrational and non-ideal configurational entropy can be sampled together in one free-energy calculation by combining nonequilibrium thermodynamic integration with an alchemical interpolation that continuously converts one species into another, interspersed with Monte Carlo identity-exchange moves that reshuffle atomic species at fixed positions. Applying this to Au-Cu using ACE potentials trained on LDA, PBE, and r2SCAN, the authors construct full composition-temperature phase diagrams directly from atomistic free energies. The headline result is that explicit configurational sampling lowers the AuCu order-disorder transition from 818 K to 721 K for ACE-LDA","pith_inferences":["A direct test of the double-counting question is to recompute the mixing free energy with the analytic ideal-mixing term omitted; the same alchemical path with identity swaps should then return the ideal term automatically if the bookkeeping is sound.","If the method holds, the roughly 100 K shift from configurational entropy should grow in alloys with stronger short-range order or larger size mismatch; AuCu is a mild case, so more dramatic widening of solid-solution fields may appear elsewhere.","The method's per-point hysteresis could be exploited for adaptive placement of free-energy calculations, focusing computational effort near the phase boundaries rather than on a uniform grid.","The Au3Cu discrepancy being independent of the entropy treatment points to the functional as the limiting factor for this system; a potential trained on hybrid or RPA-level energetics would be a direct follow-up."],"forward_implications":["If the bookkeeping is consistent, the 97 K downward shift is a direct measure of non-ideal configurational entropy in the AuCu solid solution, which ideal-mixing treatments miss.","The widened stability fields mean ordered compounds like AuCu, AuCu3, and Au4Cu2 acquire finite solubility ranges at temperature, changing predicted phase fractions and tie-lines.","The method yields per-point free energies with forward/reverse hysteresis as an uncertainty estimate, so phase boundaries can be assigned uncertainty in composition-temperature space.","The framework extends to more than two species and to disorder within stoichiometric phases, so the same path can be reused for higher-component alloys.","Functional sensitivity of several hundred kelvin implies that atomistic phase-diagram predictions should be reported across functionals, not only for one exchange-correlation approximation."],"fun_headline_variants":["Explicit entropy sampling drops AuCu transition to 721 K","Identity swaps align AuCu phase diagram with experiment","AuCu order-disorder: 97 K closer to reality with entropy","Sampling both entropies nails AuCu transition temperature","Alchemical swaps sharpen alloy phase diagrams"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The calculation adds an analytic ideal-mixing entropy term while the simulation at the starting point already randomly rearranges atomic species among sites; if that rearrangement already accounts for all species arrangements, the mixing entropy could be counted twice.","fun_headline_variants_meta":{"raw":{"variants":["Explicit entropy sampling drops AuCu transition to 721 K","Identity swaps align AuCu phase diagram with experiment","AuCu order-disorder: 97 K closer to reality with entropy","Sampling both entropies nails AuCu transition temperature","Alchemical swaps sharpen alloy phase diagrams"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000198,"raw_usage":{"total_tokens":1207,"prompt_tokens":751,"completion_tokens":456,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":495,"completion_tokens_details":{"reasoning_tokens":377}},"tokens_in":495,"tokens_out":456,"duration_ms":3993,"temperature":1.0,"reasoning_tokens":377,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T01:02:56.002748+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the alchemical transformation at xCu=0.5 and 1000 K with the analytic ideal-mixing term removed from the free-energy formula. If the resulting free energy differs from the published value by k_B T ln2 per atom (about 0.060 eV/atom at 1000 K), the term was double-counted; if it agrees, the bookkeeping is consistent.","supporting_citations":[],"review_version":1}