{"id":"6c8c041d-340c-4038-93e8-e79c3fd9e580","arxiv_id":"2607.24132","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":7,"one_line_summary":"Applying Landauer's erasure bound to one-bit Hawking steps yields constraints on generalized black hole entropies, ruling out Kaniadakis entropy for nonzero deformation.","lead":"This paper uses Landauer's principle, the minimum energy cost of erasing one bit of information, as a consistency test for generalized black hole entropy formulas under area quantization. It derives parameter or temperature constraints for most models and declares Kaniadakis entropy incompatible for any nonzero deformation.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The Landauer bound is evaluated with the fixed Schwarzschild Hawking temperature for every entropy model, but modified S(M) implies a different first-law temperature T_eff=dM/dS; if T_eff is the correct environment temperature the entire classification, including Kaniadakis exclusion, does not…","rationale":"The paper's central claim is that Landauer's principle, applied to one-bit evaporation steps, imposes constraints on temperatures, masses, and model parameters, and excludes Kaniadakis entropy. The entire derivation goes through the inequality ΔM >= k_B T ln2 with T given by Eq. (22) for all models. But the same calculus that produces ΔM for each model also defines a thermodynamic temperature T_eff = dM/dS; the mass variations quoted in Eqs. (34), (54), (69), (79), (87), (93), and (102) are all of the form k_B T_eff ln2. Thus the parameter constraints and the Kaniadakis incompatibility are statements about T_eff versus T_H, not about Landauer's principle alone. If the principle's temperature is the first-law temperature, every model saturates and the classification is empty; if it is the radiation temperature, the paper has not shown that modified entropy models emit at T_H. This is the single most load-bearing assumption because it is used in every section and determines the three outcome categories. A secondary issue, the Rényi quantization parameter in Eq. (71) and its positivity analysis, is internally inconsistent and should be corrected, but it affects only one model and does not threaten the framework as a whole. Given that the temperature choice is testable and can be fixed by a clear physical justification, the reader's CONDITIONAL verdict is appropriate; I do not recommend changing it.","tokens_in":16746,"tokens_out":15576,"duration_ms":130283,"concrete_test":"Recompute every entry of Table I with T_eff = dM/dS = 1/S'(M) in the Landauer inequality instead of Eq. (22). For Kaniadakis, this gives ΔM = k_B T_eff ln2 by construction; if all models then saturate the inequality and no parameter constraints or exclusions remain, the central classification is an artifact of the fixed-T_H choice. If the authors intend the radiation temperature, the analogous test is to derive the emission temperature for each modified entropy model and show that it equals Eq. (22).","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the identification of the temperature T in the Landauer inequality (24) with the unmodified Schwarzschild Hawking temperature (22) for every entropy model. Nothing in the paper justifies this identification. For a modified entropy S(M), the first law defines a thermodynamic temperature T_eff = dM/dS = 1/S'(M), and the paper's own mass variations are exactly ΔM = k_B T_eff ln2: Eq. (69) for Rényi is ΔM = [1 + ν/(16π G k_B^2 T^2)] k_B T ln2, i.e., T_eff/T = 1 + ν/(16π G k_B^2 T^2); Eq. (102) for Kaniadakis gives T_eff/T = 1/cosh(...) < 1. If Landauer's T is T_eff, then every model saturates the bound and the Kaniadakis incompatibility disappears; if T is meant to be the radiation/environment temperature, the paper must state and defend that, because generalized entropies then generally violate the first law dM=T dS. The three-way classification in Table I depends entirely on this unresolved choice.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes to use Landauer's principle, in the form of the inequality ΔM ≥ k_B T ln 2, as a criterion for whether a proposed black hole entropy model is thermodynamically consistent. The physical picture is that each Hawking evaporation step corresponds to the erasure of one bit of horizon information. For the Bekenstein-Hawking entropy, the paper shows that the emitted energy per step saturates the bound. For a collection of generalized entropies (mass-to-horizon, corrected Bekenstein-Hawking, Rényi, Sharma-Mittal, loop-quantum-gravity, hypergeometric, and Kaniadakis), it derives constraints either on the black hole mass/temperature or on the free parameters of the entropy model, and it derives the associated area quantization parameter and relative area spectrum for the compatible models. The Kaniadakis entropy is found to be incompatible with the Landauer criterion for any nonzero deformation parameter.","tokens_in":17048,"tokens_out":14059,"duration_ms":113146,"significance":"If the framework is sound, the paper offers a systematic, information-theoretic classification of generalized black hole entropy models, with parameter constraints that are in principle falsifiable and with explicit predictions for area spectra. The authors are transparent that the one-bit erasure assumption is an input, and they derive the Landauer constraints from the principle rather than building the conclusion into the setup, which is a strength. The unified table and comparative figure are useful for assessing the models side by side. However, the significance is currently limited by several load-bearing algebraic and interpretive problems, most notably the unjustified identification of the temperature in the Landauer bound and errors in the Rényi and Sharma-Mittal derivations.","major_comments":[{"comment":"The paper evaluates the Landauer inequality using the unmodified Schwarzschild Hawking temperature T = 1/(8πG k_B M) for every entropy model, but the mass variation ΔM in each model is computed from the first-law relation ΔS = S'(M)ΔM = k_B ln 2, which by construction gives ΔM = k_B T_th ln 2 with T_th = 1/S'(M). If the temperature in the Landauer bound is meant to be this thermodynamic temperature of the modified entropy, then every model saturates the bound and none of the constraints in Table I follow; if it is meant to be the environment (radiation) temperature, that identification must be stated and defended, because the modified first law does not relate dM to T_H dS. The classification into temperature-constrained, parameter-constrained, and incompatible models depends entirely on this unresolved choice.","section":"§III, Eq. (24) and Eq. (22)"},{"comment":"Eq. (71) for the Rényi area quantization parameter is not the solution of the condition S_{n+1}-S_n = k_B ln 2. With S_n = (k_B/ν) ln(1+νγn/4), the correct solution is γ = 4(2^ν−1)/[ν(2^ν(n+1)−n)], which reduces to γ = 4 ln 2 as ν→0. The published expression instead diverges as −4/[ν(n+1)] in that limit. Consequently, the positivity analysis is internally contradictory: the statement that the numerator of Eq. (71) is always non-positive is false for 0≤ν<1/2, and the claim lim_{ν→0} 1/(2ν−1) = ∞ is incorrect (the limit is −1). Figure 1, which uses ν = 0.006, cannot be produced from Eq. (71) with positive γ, so the Rényi entries in Table I and Fig. 1 are not supported.","section":"§IV.A, Eqs. (71)–(75)"},{"comment":"The mass variation for the Sharma-Mittal entropy has the wrong exponent. From S_SM = (k_B/ϱ)[(1+ϑS_BH/k_B)^{ϱ/ϑ}−1], the derivative gives ΔM = [1+ϑ/(16πG k_B^2 T^2)]^{(ϑ−ϱ)/ϑ} k_B T ln 2, not [(1−ϱ)/ϑ] as written in Eq. (79). The derivation of the parameter constraint ϑ≥ϱ from Eqs. (80)–(82) relies on the order of the exponent, so the conclusion is not justified by the equation as printed. The correct exponent should be restored and the parameter analysis redone.","section":"§IV.B, Eq. (79)"}],"minor_comments":[{"comment":"There are numerous typographical and grammatical errors, including 'R’enyi' instead of 'Rényi' and inconsistent notation for the Sharma-Mittal parameters (ϱ, ϑ in the text but θ in the caption of Fig. 1).","section":"General"},{"comment":"The comparison of the Bekenstein-Mukhanov and Landauer approaches yields k = 2, but the paper does not discuss whether the assumption W_n = k^n with k=2 is compatible with the degeneracy structure of the area spectrum; a brief comment would help.","section":"§II, Eq. (9)"},{"comment":"The derivation of γ for the hypergeometric entropy uses an expansion to first order in ξ and ˜ϵ while neglecting O(ξ˜ϵ) terms; the regime of validity of this approximation should be stated explicitly, especially since the resulting Eq. (98) is then used to draw conclusions about the full parameter space.","section":"§IV.D, Eq. (98)"},{"comment":"The figure caption lists parameter values but does not state which entropy formula is being plotted; for the Rényi curve, the plotted γ appears incompatible with Eq. (71), so the figure should be regenerated from the corrected formulas and the caption should identify the exact expressions used.","section":"§VI, Fig. 1"},{"comment":"The inequality T < 1/|α f'(M)| is obtained under the assumption α f'(M) ≤ 0; the paper should state separately that if α f'(M) > 0, no temperature can satisfy the Landauer condition for that model, which is a distinct exclusion case rather than a bound on T.","section":"§III.B, Eq. (58)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is heavily based on the companion preprint [9] and the novel contribution is mainly the systematic application of the Landauer criterion and the comparison table. The central idea is interesting, but the current version contains multiple load-bearing errors in the Rényi and Sharma-Mittal sections, and the temperature identification in the Landauer inequality needs a clear physical justification. If the authors can correct the algebra and explicitly address the temperature issue, a revised version could be publishable; in its present form, the derived constraints and the Kaniadakis exclusion claim are not reliable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"I've read arXiv:2607.24132. It applies Landauer's principle to a large family of generalized black hole entropies and sorts them into three categories: constraints on Hawking temperature/mass, constraints on entropy parameters, and outright incompatibility (Kaniadakis). That classification is new relative to Ref. [9], and most of the algebra is straightforward and correct. The Bekenstein-Mukhanov comparison is clean, and the mass-to-horizon, Sharma-Mittal, LQG, and hypergeometric sections are workmanlike. The Kaniadakis exclusion follows directly from cosh(x) ≥ 1, and if you accept the Landauer criterion, it's a neat result.\n\nThe problems are concentrated in the Rényi section, which the paper specifically advertises as correcting Ref. [9]. Equation (71) for the area quantization parameter is wrong: it diverges as ν → 0 instead of giving 4 ln 2, and it doesn't match Fig. 1. The positivity analysis in Eqs. (72)-(74) is internally contradictory — for 0 ≤ ν < 1/2 the numerator of (71) is positive, not non-positive, and the inequality n < 1/(2ν−1) has no solutions in that range. The correct formula is γ = 4(2^ν−1)/[ν(1+n(1−2^ν))], which has the right limit and a different positivity condition. The Rényi section needs to be redone.\n\nThe deeper issue is the temperature identification. The paper plugs the standard Schwarzschild Hawking temperature (22) into the Landauer inequality for every model. That's defensible if T is the radiation temperature: Hawking radiation far away is at T_H, and Landauer's bound concerns the environment temperature. But the paper never says this explicitly. If instead one uses the effective thermodynamic temperature dM/dS, which a modified entropy implies through the first law, then every model saturates the bound and the Kaniadakis incompatibility disappears. The paper must state which T is meant and defend the choice. It also should acknowledge that keeping T_H while modifying S means those models do not satisfy the usual first law dM = T dS.\n\nThe literature coverage is adequate, with relevant references to the entropy models and Landauer literature. Who is this for? People working on generalized entropies and black hole information theory. It's a useful survey, but I wouldn't rely on the Rényi results or on the three-way classification until the temperature question is answered. It deserves peer review, not a desk reject, but the referee should be told to check the arithmetic carefully. After revision, this could be a solid, modest contribution.","headline":"Systematic but uneven application of Landauer's principle to generalized entropies; the Rényi section has real errors and the temperature choice for the Landauer bound needs explicit defense.","tokens_in":17540,"tokens_out":12396,"would_cite":false,"duration_ms":96608,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83C57","94A17"],"pacs":["04.70.-s","04.70.Dy"],"model":"deepseek-v4-flash","headline":"This paper claims that Landauer's principle — the minimum thermodynamic cost of erasing one bit — can serve as a consistency test for generalized black hole entropy formulas, classifying them into temperature-constrained…","keywords":["Landauer's principle","black hole entropy","area quantization","Hawking evaporation","generalized entropies","Kaniadakis entropy","Rényi entropy","thermodynamic consistency"],"falsifier":"Compute the thermodynamic temperature $T = dM/dS$ for each generalized entropy model instead of using the Schwarzschild formula, and re-check whether $\\Delta M \\geq k_B T \\ln 2$ holds. For Kaniadakis entropy this means testing whether a nonzero-parameter regime can satisfy the bound once the temperature is model-dependent; if such a regime exists, the paper's exclusion is an artifact of its fixed temperature.","tokens_in":16517,"feed_emoji":"🕳️","tokens_out":7304,"duration_ms":62813,"temperature":0.7,"pith_summary":"The paper tries to show that a single information-theoretic inequality — Landauer's requirement that erasing one bit dissipate at least $k_B T \\ln 2$ of heat — can serve as a physical criterion for deciding which generalized black hole entropy formulas are thermodynamically consistent. If correct, this would give a principled way to choose among competing entropy proposals purely from information cost. The claimed payoff is a classification: some entropy models are forced into restricted mass or temperature ranges, some into restricted parameter ranges, and Kaniadakis entropy is ruled out entirely except in the Bekenstein-Hawking limit. The same step also yields the horizon area quantization parameter and area spectrum for every surviving model, with a level-dependent spacing for most generalized entropies. The Bekenstein-Hawking case saturates the bound, reproducing the area spacing $\\gamma = 4\\ln 2$.","feed_headline":"Landauer bound splits black hole entropy models into three classes","feed_subtitle":"For black holes, each one-bit Hawking step must meet Landauer's minimum heat cost; Kaniadakis entropy fails.","key_machinery":"The load-bearing object is the Landauer inequality $\\Delta M \\geq k_B T \\ln 2$, combined with the identification of each downward Hawking transition with the erasure of one bit, so that $\\Delta S = k_B \\ln 2$. The argument uses the Bekenstein-Mukhanov area quantization $A_n = \\gamma l_P^2 n$ and the unmodified Schwarzschild temperature $T = 1/(8\\pi G k_B M)$. For each entropy model $S(M)$, the paper differentiates to obtain $\\Delta S = S'(M)\\Delta M$, imposes the Landauer inequality, and then either solves for allowed temperature, mass, or entropy parameters, or equates the entropy change to $k_B\\ln 2$ to obtain $\\gamma$ and the area spectrum.","core_discovery":"The paper's central claim is that Landauer's inequality $\\Delta M \\geq k_B T \\ln 2$, applied to a Schwarzschild black hole that loses one bit of information per Hawking transition between quantized area levels, is a valid thermodynamic-consistency criterion for generalized horizon entropies. Under this criterion, the Bekenstein-Hawking entropy exactly saturates the bound and yields $\\gamma = 4\\ln 2$ in the area spectrum $A_n = \\gamma l_P^2 n$, matching the Bekenstein-Mukhanov counting with $k=2$. The paper further claims that mass-to-horizon and corrected Bekenstein-Hawking entropies survive only under temperature or mass constraints; that Rényi, Sharma-Mittal, loop-quantum-gravity, and hypergeometric entropies survive only for restricted parameter values; and that Kaniadakis entropy is incompatible for any nonzero deformation parameter $\\kappa$, because the factor $\\cosh(\\kappa S_{BH}/k_B) \\geq 1$ drives the emitted energy per one-bit step below the Landauer bound.","pith_inferences":["Editorial inference: the whole classification inherits the assumption that the environment temperature is the unmodified Schwarzschild Hawking temperature; if generalized entropies imply a different thermodynamic temperature $dM/dS$, the constraints and the Kaniadakis exclusion could shift.","Editorial inference: the paper's ordering — first impose $\\Delta M \\geq k_B T \\ln 2$, then set $\\Delta S = k_B \\ln 2$ — reverses the sign of the allowed Rényi parameter relative to earlier work, suggesting that other entropy models might change classification under the same reordering.","Editorial inference: the same test could be carried over to rotating or charged black holes, where the mass-temperature relation differs, to see whether the compatibility classes remain stable."],"forward_implications":["The Bekenstein-Mukhanov quantization constant $k=2$ follows from Landauer saturation, so the two independent quantization schemes agree on $\\gamma = 4\\ln 2$.","For mass-to-horizon and corrected Bekenstein-Hawking entropies, the Landauer inequality restricts which black hole masses or temperatures are thermodynamically admissible.","For Rényi, Sharma-Mittal, loop-quantum-gravity, and hypergeometric entropies, the same inequality fixes the sign or range of the free parameters, with Rényi entropy further restricted to $0 \\leq \\nu < 1$ by the positivity of $\\gamma$.","For every compatible model, the relative area spacing $\\Delta A_n/A_n$ vanishes as $n \\to \\infty$, so the discrete area spectrum becomes effectively continuous at macroscopic scales.","Kaniadakis entropy, if the criterion is accepted, cannot describe a one-bit Hawking evaporation step for any $\\kappa \\neq 0$."],"supporting_citations":[{"why":"Supplies Landauer's principle and the per-bit erasure cost $k_B T \\ln 2$ that the paper uses as its consistency criterion.","marker":"[11]"},{"why":"Supplies the uniform area quantization $A_n = \\gamma l_P^2 n$ and the level-counting argument whose $k=2$ match is derived.","marker":"[8]"},{"why":"Prior derivation of Landauer-based area quantization for Bekenstein-Hawking and some modified entropies; the present paper changes the order of constraints for Rényi entropy.","marker":"[9]"},{"why":"Defines Rényi entropy, one of the parameter-constrained models.","marker":"[34]"},{"why":"Defines Kaniadakis entropy, the model shown incompatible with the Landauer inequality.","marker":"[25,26]"},{"why":"Defines mass-to-horizon entropy, whose temperature and mass constraints are derived.","marker":"[42,43]"},{"why":"Supplies the general corrected Bekenstein-Hawking entropy form used for the temperature-constrained class.","marker":"[31]"},{"why":"Defines Sharma-Mittal entropy, one of the parameter-constrained models.","marker":"[36]"}],"fun_headline_variants":["Landauer bound rules out Kaniadakis black hole entropy","Black hole entropy models pass or fail Landauer test","Hawking evaporation costs one bit: entropy models judged","Landauer criterion classifies black hole entropy models","Information erasure constrains black hole entropy formulas"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The analysis evaluates every generalized entropy with the unmodified Schwarzschild Hawking temperature $T = 1/(8\\pi G k_B M)$; if the true environment temperature is instead $dM/dS$ for the modified entropy, the derived constraints and the exclusion of Kaniadakis entropy do not follow.","fun_headline_variants_meta":{"raw":{"variants":["Landauer bound rules out Kaniadakis black hole entropy","Black hole entropy models pass or fail Landauer test","Hawking evaporation costs one bit: entropy models judged","Landauer criterion classifies black hole entropy models","Information erasure constrains black hole entropy formulas"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000278,"raw_usage":{"total_tokens":1680,"prompt_tokens":999,"completion_tokens":681,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":615,"completion_tokens_details":{"reasoning_tokens":605}},"tokens_in":615,"tokens_out":681,"duration_ms":6216,"temperature":1.0,"reasoning_tokens":605,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T15:27:34.325259+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the thermodynamic temperature $T = dM/dS$ for each generalized entropy model instead of using the Schwarzschild formula, and re-check whether $\\Delta M \\geq k_B T \\ln 2$ holds. For Kaniadakis entropy this means testing whether a nonzero-parameter regime can satisfy the bound once the temperature is model-dependent; if such a regime exists, the paper's exclusion is an artifact of its fixed temperature.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies Landauer's principle and the per-bit erasure cost $k_B T \\ln 2$ that the paper uses as its consistency criterion."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the uniform area quantization $A_n = \\gamma l_P^2 n$ and the level-counting argument whose $k=2$ match is derived."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Prior derivation of Landauer-based area quantization for Bekenstein-Hawking and some modified entropies; the present paper changes the order of constraints for Rényi entropy."},{"cited_title":"Banerjee, B","cited_arxiv_id":null,"evidence_quote":"Supplies the general corrected Bekenstein-Hawking entropy form used for the temperature-constrained class."},{"cited_title":"Majhi, Non-extensive statistical mechanics and black hole entropy from quantum geometry, Phys","cited_arxiv_id":null,"evidence_quote":"Defines Sharma-Mittal entropy, one of the parameter-constrained models."}],"review_version":2}