{"id":"b6eb4b1b-0319-4e48-9cae-d2302088e8b5","arxiv_id":"2507.13412","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A Carnot information engine is claimed to reach 100% efficiency, but only under an efficiency accounting that excludes the thermodynamic cost of information.","lead":"This paper adds a measurement and feedback step to a standard Carnot cycle and claims the resulting information-assisted engine can beat the Carnot efficiency and even reach 100%. The claim depends on a non-standard efficiency definition that treats the demon's work as input energy and does not count the cost of processing information.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed 100% efficiency and surpassing of thermodynamic bounds rely on excluding the information reservoir from the energy balance; the paper itself acknowledges this at Eq. (A5), so the headline overstates what the model shows.","rationale":"The central claim—that the CIE can reach 100% efficiency with positive work and thereby surpass standard thermodynamic bounds—is only true if the information used by the demon is free and if the demon's memory does not have to be reset. The paper's own Appendix A, Eq. (A5), computes σ = I_C' for the composite system and calls the process irreversible due to information dissipation, and Appendix B's defense of the efficiency definition is about distinguishing demon work from system work, not about accounting for the demon's reset. The reader's weakest_assumption identifies exactly this omission, and I agree with the reader's REJECT. I do not see an internal inconsistency in the algebra; the issue is that Eqs. (5)-(9) describe an open subsystem, not a complete cyclic engine. A reviewer could reasonably accept the paper as a model of an information-assisted engine if the information reservoir were explicitly declared a free resource, but the abstract and conclusions claim 'breaking efficiency limits of conventional heat engines' and 'dissipationless heat engines' without that caveat. Given the field's consensus that Landauer erasure must be included in a full accounting, the headline is overstated. The concrete test above would settle the matter: adding the erasure cost to the denominator directly removes the 100% point and would make the claimed bound dependent on a free resource.","tokens_in":17207,"tokens_out":12463,"duration_ms":149547,"concrete_test":"Add one stroke to the model that resets the demon memory at the end of stroke D'→A, using the state probabilities in Appendix A to compute I_C' = S_Y - S_h. Evaluate the closed-cycle efficiency η_closed = W_d^tot / (Q_h + W_d + W_landauer), where W_landauer = β_c^{-1} I_C' is the minimal erasure work at the cold-bath temperature (or β_d^{-1} I_C' if the memory is erased at its own temperature). Recalculate at the S_ε = S_c operating point used for the 100% claim; if η_closed < 1 and, after also charging the measurement apparatus, the engine does not exceed the Carnot efficiency, the central claim depends on the free-information assumption. This is a one-line modification of Eqs. (5)-(9) and requires no simulation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing assumption is that Eq. (8) is a valid closed-cycle efficiency. The denominator Qd_h = Qh + Wd counts only hot-reservoir heat and demon work on the working system, and Eq. (5) uses the cold reservoir only for the working-system entropy change. It does not include the entropy left in the demon's memory. Appendix A explicitly defines the total microscopic entropy production of the complete system as σ = IC' ≠ 0 and identifies 'information dissipation' in the composite system. Since the demon must be reset for the engine to operate cyclically, erasing that memory costs work: at least β_c^{-1} I_C', or more generally the Landauer cost of the stored information. If that cost is included in the denominator, the 100% point S_ε = S_c no longer yields η = 1; the heat formerly dumped in the cold reservoir is replaced by information dumped in the memory, so the process is not dissipationless. Therefore the qualitative conclusion that the CIE 'surpasses standard thermodynamic bounds' is not supported against all inputs; it is a statement about a subsystem with an unpaid information debt. This is a concern about interpretation, not about the internal algebra of Eqs. (1)-(9), which appears consistent.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript introduces a 'Carnot information engine' (CIE), a two-level system operating through two standard Carnot strokes followed by a measurement-feedback control and a cold isothermal return. The central results are Eq. (8), η_d = W_tot^d/(Q_h+W_d) = η_C + (β_h W_d − ΔI)/(β_c Q_d^h), and the inequalities η_C ≤ η_d ≤ η_up derived from β_h W_d ≥ ΔI ≥ β_d W_d. The authors argue that information changes allow the engine to operate in a regime forbidden to the standard Carnot cycle and to reach η_d = 1 when Q_d^c = 0. A spin-1/2 example and a trapped-ion implementation are presented.","tokens_in":17503,"tokens_out":21535,"duration_ms":249986,"significance":"The algebraic framework is transparent and largely self-consistent: the key inequality β_h W_d ≥ ΔI follows from a second-law argument in Appendix C, and the spin-1/2 example gives explicit curves for work, heat, and efficiency. The proposed trapped-ion experiment is a concrete and potentially falsifiable setup. However, the paper's significance as stated is undermined by the efficiency accounting: the information reservoir is not included in the energy balance, and the 100% efficiency claim is therefore a statement about a subsystem with an unpaid information debt rather than a full-cycle thermodynamic bound.","major_comments":[{"comment":"The headline claims that the CIE 'surpasses standard thermodynamic bounds' and 'achieves 100% efficiency' are not supported as full-cycle statements. The efficiency in Eq. (8) counts only Q_h and W_d in the denominator and omits the cost of the information reservoir. Appendix A explicitly computes the total microscopic entropy production of the complete system as σ = I_C' ≠ 0 and attributes it to 'information dissipation.' For a cyclic engine the demon's memory must be reset, and the minimum erasure work is at least β_c^{-1} I_C' (or the corresponding Landauer cost). When this cost is included, the point S_ε = S_c no longer gives η = 1: the heat formerly rejected to the cold reservoir is replaced by information discarded from the memory, so the cycle is not dissipationless. The results should be explicitly presented as a partial efficiency of the working fluid relative to a free information reservoir, with the full accounting made elsewhere.","section":"Conclusions; Eq. (8); Appendix A, Eq. (A5)"},{"comment":"The definition of Q_d^h = Q_h + W_d as 'total invested energy' is problematic when the demon's work is negative, which can occur at the 100% point (in the spin-1/2 example, S_ε = S_c gives a small ε and W_d = ω_C(ε − P_C^e) < 0). The same W_d enters the numerator W_tot^d through W_net, so a negative W_d simultaneously reduces the denominator and the numerator, and η_d = 1 is an artifact of subtracting the demon's extracted work from the input while still counting it (with opposite sign) in the output. If the demon is a work source, W_d should be an input; if it extracts work, that extraction should be counted as output without subtracting it from the heat input. The efficiency definition should be justified for both signs of W_d.","section":"Eq. (8); Appendix B"},{"comment":"The inequality β_h W_d ≥ ΔI, which drives η_d ≥ η_C, is proved by considering a fictitious isochoric thermalization of the post-feedback distribution back to the hot reservoir at frequency ω_C. This is a free-energy inequality for the working system alone and does not involve the information reservoir. The statement that 'information changes' cause the efficiency to exceed the Carnot value is therefore a subsystem-level result; it does not represent a violation of a global second-law bound. The authors should state this distinction explicitly.","section":"Eq. (9); Appendix C"}],"minor_comments":[{"comment":"The notation S_c for the entropy at points A and B and S_h for the entropy at point C is not defined explicitly in the main text, which is confusing because the subscript 'c' also denotes the cold reservoir; please add a sentence defining these symbols.","section":"Main text, Eqs. (1)-(5)"},{"comment":"Equation (E2) contains a misplaced parenthesis in 'ωC(⟨nd⟩) − ⟨nh⟩)' which should read 'ωC(⟨nd⟩ − ⟨nh⟩)'; in the same appendix, '⟨nd⟩ ≤ ⟨nd⟩' should be '⟨nd⟩ ≤ ⟨nh⟩' and '⟨nd⟩ > ⟨nd⟩' should be '⟨nd⟩ > ⟨nh⟩'.","section":"Appendix E, Eq. (E2)"},{"comment":"The caption calls Q_d^c the 'absorbed heat from the cold reservoir,' but in the extended-regime discussion Q_d^c < 0; please reword to avoid sign confusion (e.g., 'heat exchange with the cold reservoir').","section":"Fig. 2 caption"},{"comment":"The last equality of Eq. (5) uses the stochastic entropy-flow formula of Ref. [32]; because that reference is a self-citation, a one-line derivation or statement of the formula would make the paper more self-contained.","section":"Eq. (5), Appendix A"}],"recommendation":"major_revision","confidential_remarks":"The paper's central conclusion is overstated: without a full accounting of the information reservoir, the title and abstract are misleading. The underlying algebra appears sound and the model is clearly presented, so a substantial revision that reframes the claims as a partial efficiency analysis and explicitly derives the full efficiency including erasure could make the paper acceptable. I would not support acceptance in the current form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The short version: the model and algebra are fine, but the central claim that the engine surpasses the Carnot bound and reaches 100% efficiency rests on an efficiency definition that leaves the information reservoir out of the energy balance. Appendix A itself shows the total entropy production of the composite system is σ = I_C' ≠ 0, i.e., there is information dissipation. So the cycle is not dissipationless; the 100% point just trades heat dumped to the cold reservoir for information dumped into the demon's memory. If you include the Landauer erasure cost of that memory, the efficiency drops below 1 and the \"beyond Carnot\" claim becomes a bookkeeping artifact rather than a new physical bound.\n\nWhat's genuinely useful: the paper constructs a concrete five-stroke feedback Carnot cycle and derives clean explicit relations between mutual information changes, work output, and efficiency. The bound η_d ≥ η_C follows from a second-law inequality β_h W_d ≥ ΔI, and the derivation is internally consistent. The spin-1/2 example and trapped-ion implementation give the work a concreteness that similar papers often lack. The citation pattern is fine; Sagawa-Ueda and Fadler et al. are acknowledged, and the paper is best read as an extension of those results rather than a departure.\n\nThe soft spot is exactly where the reader puts it: the efficiency definition in Eq. (8) counts Q_h + W_d as input but not the cost of measurement, memory storage, or erasure. Appendix B's justification leans on an analogy to ergotropy, but that analogy doesn't cover the demon's memory over repeated cycles. The authors are aware of this; Appendix A even flags σ = I_C' ≠ 0. So the overstatement is in the abstract and conclusions, not in the technical core. I'd suggest the authors rephrase the claims: the CIE can exceed the standard Carnot efficiency relative to a subsystem accounting that excludes information costs, not in a closed-cycle accounting.\n\nVerdict: worth a serious referee. The algebra is consistent, the experimental scheme is detailed, and the issue is interpretational; a competent referee could get the authors to fix the overclaims. But I would not cite the 100% efficiency claim as stated, and I would not bring it to a reading group as a breakthrough.","headline":"The algebra is fine and the model is a legitimate extension of information-thermodynamics, but the headline claims of surpassing Carnot and reaching 100% efficiency rest on an efficiency definition that excludes the demon's memory cost, so the abstract overstates what the paper actually shows.","tokens_in":17994,"tokens_out":2355,"would_cite":false,"duration_ms":27103,"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 grafting an imperfect measurement-and-feedback stroke onto the standard Carnot cycle, this paper derives exact relations tying the engine's output work and efficiency to the change in mutual information $\\Delta I$, proving the engine…","keywords":["information engine","Maxwell's demon","Carnot cycle","feedback control","mutual information","quantum thermodynamics","two-level system","efficiency bound"],"falsifier":"In the proposed trapped-$^{40}\\mathrm{Ca}^+$ implementation, measure over many cycles the average work stored in the motional mode and the heats exchanged with the hot and cold reservoirs, and check whether $\\eta_d = W_{\\rm tot}^d/(Q_h + W_d)$ is always at least the Carnot efficiency and reaches 1 with $W_{\\rm tot}^d = Q_h^d$ at the $S_\\epsilon = S_c$ point; a single violation rejects the central claim.","tokens_in":17006,"feed_emoji":"⚙️","tokens_out":9959,"duration_ms":95027,"temperature":0.7,"pith_summary":"This paper claims that a standard Carnot cycle, upgraded with an imperfect classical measurement and a feedback-control stroke, can exceed the efficiency limits of conventional heat engines. The central result is a set of exact relations expressing the engine's output work and efficiency in terms of the change in mutual information between the working system and the demon's memory: the engine can operate as a heat engine in regimes where the standard Carnot cycle is thermodynamically forbidden, its efficiency is always at least the Carnot efficiency, and it can reach 100% efficiency with positive work output for arbitrary two-level systems. These features are demonstrated explicitly on a spin-1/2 working substance, and an experimental implementation with a trapped calcium ion is proposed. If the derivation is correct, information becomes a quantified, controllable resource that can be traded for work beyond the Carnot bound.","feed_headline":"Carnot engine with feedback hits 100% efficiency","feed_subtitle":"A measurement-and-feedback step lets a two-level engine beat the Carnot bound and run where standard cycles cannot.","key_machinery":"Load-bearing is the five-stroke Carnot information engine (CIE) cycle, which appends a measurement-and-feedback stroke $C \\to C'$ (with imperfect measurement error $\\epsilon$), an adiabatic expansion $C' \\to D'$, and a cold-reservoir compression $D' \\to A$ to the standard four-stroke Carnot cycle. The central quantity is the mutual information between the working system and the demon's memory, $I_C = S_Y - S_\\epsilon$ before the control stroke and $I_{C'} = S_Y - S_h$ after it, so the information change is $\\Delta I = I_{C'} - I_C = S_\\epsilon - S_h$. All performance measures are expressed through $\\Delta I$ and the demon's work $W_d = \\omega_C(\\langle n_d\\rangle - \\langle n_h\\rangle)$: the cold-reservoir heat decomposes as $Q_c^d = Q_c - \\beta_c^{-1}\\Delta I$, the net information-cycle work is $W_{\\rm net} = W_d - \\beta_c^{-1}\\Delta I$, and the efficiency bound $\\eta_C \\le \\eta_d \\le \\eta_{\\rm up}$ follows from the inequality $\\beta_h W_d \\ge \\Delta I \\ge \\beta_d W_d$ proved in Appendix C.","core_discovery":"On the paper's own terms, the discovery is that adding a demon-controlled stroke to a Carnot cycle converts mutual information between system and demon into a tunable thermodynamic resource. The efficiency is derived as $\\eta_d = \\eta_C + \\frac{(\\beta_h/\\beta_c)W_d - \\Delta I}{Q_h^d}$, where $W_d$ is the work the demon does on the system, $\\Delta I = S_\\epsilon - S_h$ is the change in mutual information (the measurement-error entropy minus the hot-reservoir entropy), and $Q_h^d = Q_h + W_d$ is the total input energy. Together with the inequality $\\beta_h W_d \\ge \\Delta I \\ge \\beta_d W_d$, this gives the efficiency bounds $\\eta_C \\le \\eta_d \\le \\eta_{\\rm up}$. When the measurement error is tuned so that $S_\\epsilon = S_c$, the engine absorbs zero heat from the cold reservoir, $Q_c^d = 0$, and the total output work equals the total input energy, $W_{\\rm tot}^d = Q_h^d \\ge 0$, so $\\eta_d = 1$ with positive work. The same relations show that in the regime $S_h < S_c < S_\\epsilon$ the CIE produces positive total work where the standard Carnot engine's work $W_{\\rm tot}$ is negative.","pith_inferences":["The paper's 100% efficiency is reached under its definition that counts only $Q_h + W_d$ as input; if the full thermodynamic cost of measurement, memory, and erasure is included, the effective efficiency would be lower, so the claim should be read as a bound on converting information-assisted input, not on all physical resources.","Since the derivation works with population entropies and level spacings rather than any spin-specific detail, the same formulas should extend to multi-level or continuous working systems; a direct test would be measuring $\\eta_d$ versus $\\Delta I$ in a trapped ion and comparing with Eq. (8).","A practical design rule suggested by the result is to tune the measurement error $\\epsilon$ so that $S_\\epsilon$ matches the cold-reservoir entropy $S_c$, which the paper shows is the condition for reaching unit efficiency."],"forward_implications":["In the parameter regime $S_h < S_c < S_\\epsilon$, the CIE produces positive total work while the standard Carnot cycle would consume work, so information feedback extends the operating range of heat engines.","The efficiency inequality $\\eta_d \\ge \\eta_C$ holds for all measurement errors, with equality only when $\\Delta I = 0$; any nonzero information change improves efficiency.","At the special point $S_\\epsilon = S_c$, the cold-reservoir heat vanishes and the engine converts all input energy $Q_h + W_d$ into output work, giving $\\eta_d = 1$ with positive work for any two-level system.","For the spin-1/2 example, the efficiency reaches a minimum at $\\beta_h = \\beta_c \\omega_A / \\omega_C$ and increases as $|\\Delta I|$ grows away from zero, and the paper proposes a trapped-$^{40}\\mathrm{Ca}^+$ ion experiment that could realize the cycle."],"supporting_citations":[{"why":"Supplies the discrete-feedback second-law bound that the CIE's efficiency inequality extends to the Carnot cycle.","marker":"[29]"},{"why":"Provides the stochastic entropy-flow expression used to compute the heat $Q_c^d$ absorbed from the cold reservoir.","marker":"[32]"},{"why":"Gives the heat absorption formula $Q_h = \\beta_h^{-1}(S_C - S_B)$ for the isothermal expansion stroke.","marker":"[45]"},{"why":"Defines the mutual information used to write $I_C$ and $I_{C'}$ for the system-demon correlation.","marker":"[53]"},{"why":"Presents a comparable Carnot quantum information engine; its efficiency definition and upper bound are discussed in Appendix B as a reference point.","marker":"[12]"},{"why":"Justifies defining engine efficiency as work output divided by total invested energy, including ergotropy, adopted for the CIE.","marker":"[54]"},{"why":"Together with [54], supports the efficiency definition by treating the demon's work as invested energy rather than output.","marker":"[55]"}],"fun_headline_variants":["Feedback Carnot engine reaches 100% efficiency","Information-assisted Carnot surpasses standard limits","Demon-controlled stroke lets engine beat Carnot","Mutual info converts to work beyond Carnot bound"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The results assume that the measurement, the memory that stores it, and the erasure of that memory are free, so the 100% efficiency counts only the hot-reservoir heat plus the demon's direct work as input; if the information reservoir carries any thermodynamic cost, the efficiency relative to all inputs cannot reach one.","fun_headline_variants_meta":{"raw":{"variants":["Feedback Carnot engine reaches 100% efficiency","Information-assisted Carnot surpasses standard limits","Demon-controlled stroke lets engine beat Carnot","Mutual info converts to work beyond Carnot bound"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000185,"raw_usage":{"total_tokens":1325,"prompt_tokens":952,"completion_tokens":373,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":568,"completion_tokens_details":{"reasoning_tokens":315}},"tokens_in":568,"tokens_out":373,"duration_ms":4165,"temperature":1.0,"reasoning_tokens":315,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T16:38:06.514066+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"In the proposed trapped-$^{40}\\mathrm{Ca}^+$ implementation, measure over many cycles the average work stored in the motional mode and the heats exchanged with the hot and cold reservoirs, and check whether $\\eta_d = W_{\\rm tot}^d/(Q_h + W_d)$ is always at least the Carnot efficiency and reaches 1 with $W_{\\rm tot}^d = Q_h^d$ at the $S_\\epsilon = S_c$ point; a single violation rejects the central claim.","supporting_citations":[{"cited_title":"Wen, Maxwell’s demon at work: mitochondria, the or- ganelles that convert in formation into energy? Chronic Dis","cited_arxiv_id":null,"evidence_quote":"Supplies the discrete-feedback second-law bound that the CIE's efficiency inequality extends to the Carnot cycle."},{"cited_title":"Serreli, C","cited_arxiv_id":null,"evidence_quote":"Provides the stochastic entropy-flow expression used to compute the heat $Q_c^d$ absorbed from the cold reservoir."},{"cited_title":"Cottet, S","cited_arxiv_id":null,"evidence_quote":"Gives the heat absorption formula $Q_h = \\beta_h^{-1}(S_C - S_B)$ for the isothermal expansion stroke."},{"cited_title":"An energy efficient quantum-enhanced machine","cited_arxiv_id":"2404.15075","evidence_quote":"Defines the mutual information used to write $I_C$ and $I_{C'}$ for the system-demon correlation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Presents a comparable Carnot quantum information engine; its efficiency definition and upper bound are discussed in Appendix B as a reference point."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Justifies defining engine efficiency as work output divided by total invested energy, including ergotropy, adopted for the CIE."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Together with [54], supports the efficiency definition by treating the demon's work as invested energy rather than output."}],"review_version":1}