{"id":"57db1988-d54f-42dd-969c-68cc0e075c30","arxiv_id":"2412.14156","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Applying Landauer's principle to black hole entropy reproduces the standard Immirzi parameter, while Barrow and modified Kaniadakis entropies make the parameter depend on horizon area.","lead":"Using the Landauer principle, the physics of how much heat is released when one bit is erased, this paper computes the Immirzi parameter, a free constant in loop quantum gravity. It reproduces the standard value and then derives area-dependent versions for two alternative black hole entropy models.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'without BG' claim is unsupported because the Landauer input ΔS=k_B ln2 is the BG two-state entropy; the same equality is applied to non-extensive entropies without justification.","rationale":"The reader's weakest assumption identifies the unproven identification of one bit erasure with one spin-1/2 puncture and flags the possibility that the saturated equality fails in non-extensive frameworks. My concern is the same one, sharpened: the Landauer input ΔS = k_B ln2 is not an independent principle but the BG entropy of a two-state system, so the derivation of Eq. (19) is algebraically identical to the standard BG counting. The novel Barrow and Kaniadakis results inherit this problem and add a new one, since the Landauer bound for non-extensive entropies is never derived. These are load-bearing issues for the paper's central claims, but they do not make the numerical value of γ wrong under standard assumptions, nor do they invalidate the internal algebra. The appropriate response is a CONDITIONAL verdict, matching the reader's. The concrete test proposed—computing the actual Landauer bound for Kaniadakis entropy—would settle whether the modified-entropy formulas (23) and (31) are valid, and would also clarify whether the 'without BG' claim can be sustained in any strict sense.","tokens_in":8163,"tokens_out":23832,"duration_ms":201066,"concrete_test":"Derive the Landauer bound for a two-state memory reset when the environment's thermodynamic entropy is the Kaniadakis entropy S_κ of Eq. (25), by minimizing the free energy F = E − T S_κ over the two-state configuration space. Compute the minimal entropy increase ΔS_min required to erase one bit. If ΔS_min depends on κ and differs from k_B ln2, then the step ΔS = k_B ln2 in Eq. (30) is unjustified, and γ_MKE in Eq. (31) must be recomputed with the corrected bound; verify that the κ→0 limit still recovers γ = ln2/(π√3).","verdict_should_be":"UNCHANGED","load_bearing_attack":"Landauer's principle is an inequality, ΔS ≥ k_B ln2, but Eq. (12) uses the saturated equality. The value k_B ln2 is precisely the Boltzmann-Gibbs entropy of a two-state system, and in LQG it equals the entropy gain from a single spin-1/2 puncture. Equating ΔA from the Bekenstein-Hawking law (Eq. (17)) to the area quantum a(1/2) (Eq. (18)) therefore imports the same W=2^N microstate counting that the abstract claims to avoid. This is not an independent derivation of γ; it is the Dreyer/BG calculation rewritten in information-theoretic language. The paper itself concedes this equivalence in Sec. 2, yet the abstract still claims 'without using the typical procedure that involves the Boltzmann-Gibbs entropy.' The same saturated equality is then applied to Barrow and Kaniadakis entropies (Eqs. (22) and (30)) without deriving the Landauer bound for those non-extensive frameworks. For such entropies, one bit of information erasure does not necessarily correspond to ΔS = k_B ln2; e.g., S_κ is not proportional to ln W, so the entropy change per bit is model-dependent. If the actual Landauer bound in these frameworks differs from k_B ln2, Eqs. (23) and (31) are not derived.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper applies Landauer's principle to derive the Immirzi parameter in Loop Quantum Gravity, obtaining γ = ln 2/(π√3) in Sec. 2, and then extends the same procedure to Barrow entropy and a modified Kaniadakis entropy, obtaining area-dependent expressions γ_B and γ_MKE in Eqs. (23) and (31). The stated novelty is that the derivation avoids the usual Boltzmann-Gibbs microstate counting. The paper also notes in Sec. 4 that the area-dependent expressions should be interpreted as effective quantities because a varying Immirzi parameter is inconsistent with the canonical structure of LQG.","tokens_in":8477,"tokens_out":3162,"duration_ms":30174,"significance":"If the derivation were an independent route to the Immirzi parameter, it would be a notable conceptual result connecting information thermodynamics and quantum geometry. The paper has clear strengths: the algebraic steps in Eqs. (22)-(23) and (29)-(31) are straightforward and correct, the limits Δ→0 and κ→0 recover the standard value, and the authors explicitly acknowledge in Sec. 4 that area-dependent γ conflicts with LQG and should be read as effective. However, as I argue below, the central claim of independence from Boltzmann-Gibbs entropy is not supported, and the non-extensive extensions assume rather than derive the relevant Landauer bound. The paper is best read as a consistency check or reformulation of the standard Dreyer calculation, not as a parameter-free derivation.","major_comments":[{"comment":"The claim that the derivation avoids the Boltzmann-Gibbs entropy is not supported. The saturated Landauer equality ΔS = k_B ln 2 in Eq. (12) is exactly the BG entropy change of a two-state system, and for a spin-1/2 puncture the LQG entropy contribution is also k_B ln 2 under the standard counting W = (2j_min+1)^N. Equating ΔA = 4 l_p^2 ln 2 from the Bekenstein-Hawking law with the area quantum a(1/2) = 4π l_p^2 γ√3 is algebraically identical to setting S_BH = N k_B ln 2 with N = A/a(1/2), which is the Dreyer/BG calculation. Thus Eq. (19) is a reformulation of the standard counting, not an independent derivation, and the abstract's phrase 'without using the typical procedure that involves the Boltzmann-Gibbs entropy' should be substantially tempered.","section":"Sec. 2, Eqs. (12)-(19)"},{"comment":"The paper applies the saturated Landauer equality ΔS = k_B ln 2 to Barrow entropy and modified Kaniadakis entropy without deriving or justifying the Landauer bound for those non-extensive frameworks. For Kaniadakis entropy in particular, Eqs. (24)-(25) show that S_κ is not proportional to ln W, so erasing one bit of information does not automatically correspond to an entropy change of k_B ln 2; the entropy change per bit is generally model-dependent. Unless the Landauer bound for these entropies is established, Eqs. (23) and (31) rest on an additional assumption and are not derived consequences of the stated principles. This is load-bearing for the paper's main new results.","section":"Secs. 3 and 4, Eqs. (22)-(23) and (30)-(31)"},{"comment":"The abstract and the main text (e.g., Eq. (23) and Fig. 1) present γ_B and γ_MKE as 'Immirzi parameter' values, while Sec. 4 concedes that an area-dependent γ is inconsistent with LQG and should be interpreted as an effective quantity. This qualifier is essential and should appear wherever the symbols are introduced and in the abstract; currently the abstract presents the results without that caveat, which is misleading about the physical status of the derived expressions.","section":"Abstract and Sec. 4, final paragraph"}],"minor_comments":[{"comment":"Eq. (14) is described as Landauer's principle 'when it is saturated'; it would be helpful to state explicitly that this follows from combining the Bekenstein-Hawking relation with the assumption that erasing one bit removes exactly one unit of entropy k_B ln 2, since that assumption is the operative input.","section":"Sec. 2, around Eq. (12)"},{"comment":"The notation S_BH is used in Eq. (26) before it is defined in the following line; reorder or define it explicitly at first use.","section":"Sec. 4, Eq. (26)"},{"comment":"The paper should clarify whether S_κ^* is intended as a new black-hole entropy formula or as an effective parametrization; the text says both things at different points, and a single consistent statement would avoid confusion.","section":"Sec. 4, Eq. (28)"},{"comment":"The y-axis labels 'Immirzi parameter' should be changed to 'effective Immirzi parameter' to match the caveat in Sec. 4, and the captions should state that the plotted quantities are area-dependent effective parameters.","section":"Figs. 1 and 2"}],"recommendation":"major_revision","confidential_remarks":"The manuscript's central novelty is the claim of deriving the Immirzi parameter without Boltzmann-Gibbs entropy, but the derivation is algebraically equivalent to the standard Dreyer calculation. The non-extensive results are conditional on an unjustified Landauer bound for Barrow and Kaniadakis entropies. These issues are fixable by reframing the paper as a consistency check and by explicitly deriving or clearly postulating the generalized Landauer bounds, but as it stands the main claims overstate what has been shown."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nTwo things to know off the bat. First, the paper's central derivation – Eqs. (12)–(19) – does exactly what it says algebraically: using the saturated Landauer equality ΔS = k_B ln2 together with the LQG area quantum for j=1/2 gives the standard Immirzi value. Second, the advertised novelty over Boltzmann-Gibbs counting is not real. k_B ln2 is the BG entropy of a two-state system, and the microstate counting W = 2^N is sitting right in the paper's own Sec. 2. The Landauer route is a repackaging of Dreyer's count, not an independent derivation.\n\nWhat is actually new are the two area-dependent expressions, Eq. (23) for Barrow entropy and Eq. (31) for modified Kaniadakis entropy. The algebra checks; the limits Δ→0 and κ→0 recover the standard γ. The paper also deserves credit for flagging in Sec. 4 that a running γ is inconsistent with LQG's canonical structure and should be treated as an effective quantity. That caveat is prominent enough that the abstract's unqualified claim about deriving \"the Immirzi parameter\" in those frameworks is the main overreach. The abstract should carry the same qualifier.\n\nThe soft spots are all interpretive. The stress-test note is right: Landauer is an inequality, and the paper uses saturation without independent justification. For the non-extensive entropies, the paper simply reuses ΔS=k_B ln2, but the Landauer cost per bit in Barrow or Kaniadakis statistics is not derived; it is assumed. So Eqs. (23) and (31) are conditional on a premise that may fail in those frameworks. Also, the paper does not sharply delineate what is new relative to ref. [20], which already applies Landauer to area quantization. The Sec. 2 result seems to be the same constraint.\n\nNone of this is fatal. The paper is short, readable, and honest about its limitations. The formulas (23) and (31) are new enough to be of use to people working on corrections to black-hole entropy. I would take it as a modest but legitimate contribution in a crowded field: the derivation of γ is not new in substance, but the Barrow/Kaniadakis applications are.\n\nSend it to a referee, yes. The referee's main job is to pin down what is actually new versus [20] and to make the authors add the effective qualifier to the abstract. It deserves a serious referee, even if the expected outcome is a revised, more carefully framed paper.","headline":"Landauer-based Immirzi derivation reproduces the standard value but the 'no Boltzmann-Gibbs' claim doesn't survive the equations; the new Barrow/Kaniadakis formulas are honest algebra with an effective-quantity caveat.","tokens_in":9045,"tokens_out":2700,"would_cite":false,"duration_ms":21264,"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":"This paper derives the Immirzi parameter of Loop Quantum Gravity from the Landauer principle alone, obtaining exactly $\\gamma = \\ln 2/(\\pi\\sqrt{3})$ without Boltzmann-Gibbs microstate counting.","keywords":["Immirzi parameter","Landauer principle","Loop Quantum Gravity","Bekenstein-Hawking entropy","Barrow entropy","Kaniadakis entropy","black hole information","area quantization"],"falsifier":"Measure or compute the area change that accompanies a one-bit loss of information from a black hole horizon. If it is not $4l_p^2\\ln2$, for instance if it is a multiple of that or depends on the horizon area, then equating it to the single spin-1/2 puncture quantum $4\\pi l_p^2\\gamma\\sqrt3$ fails and the derived $\\gamma$ cannot be sustained. Within LQG itself, a calculation showing that macroscopic black hole entropy is dominated by punctures with $j>1/2$ would equally falsify the identification used here.","tokens_in":7890,"feed_emoji":"🕳️","tokens_out":7292,"duration_ms":59023,"temperature":0.7,"pith_summary":"This paper tries to show that the Immirzi parameter of Loop Quantum Gravity, a free constant governing the area spectrum, can be fixed by an information-theoretic argument instead of the usual counting of gravitational microstates. The route is Landauer's principle: erasing one bit of black hole information costs entropy $\\Delta S = k_B \\ln 2$, and when that loss is written through the Bekenstein-Hawking area law it fixes the area change to $\\Delta A = 4 l_p^2 \\ln 2$. Equating that change with the smallest LQG area quantum, $a(1/2)=4\\pi l_p^2 \\gamma \\sqrt{3}$, gives exactly $\\gamma = \\ln 2/(\\pi\\sqrt{3})$, the same value obtained from Boltzmann-Gibbs counting. The same procedure is then run inside Barrow and modified Kaniadakis entropy frameworks, producing new area-dependent expressions for $\\gamma$ that reduce to the standard value in the appropriate limits. The result connects black hole information erasure to the quantum geometry of loop gravity and offers a thermodynamic route into alternative entropy models.","feed_headline":"Erasing one bit fixes loop gravity's Immirzi parameter","feed_subtitle":"Equating one-bit erasure with a spin-1/2 area quantum reproduces the statistical value and yields area-dependent variants.","key_machinery":"The argument runs on three identities joined by one equality. The first is the saturated Landauer principle, $\\Delta S = k_B \\ln 2$, for erasing one bit. The second is the Bekenstein-Hawking area law, $S = k_B A/(4l_p^2)$, whose variation gives $\\Delta S = (k_B/4l_p^2)\\Delta A$. The third is the LQG area quantum for a puncture of spin $j$, $a(j) = 8\\pi l_p^2 \\gamma\\sqrt{j(j+1)}$, evaluated at the minimum spin $j=1/2$ as $a(1/2)=4\\pi l_p^2\\gamma\\sqrt{3}$. The load-bearing move is to identify the one-bit area change $\\Delta A = 4l_p^2 \\ln 2$ with $a(1/2)$, which turns the free parameter $\\gamma$ into a fixed number. For Barrow and modified Kaniadakis entropies, the same move is repeated with their modified entropy variations, Eqs. (21) and (29), which is what makes $\\gamma$ area-dependent in those frameworks.","core_discovery":"On the paper's own terms, the central discovery is that the Immirzi parameter does not need the Boltzmann-Gibbs microstate counting to be determined. Starting from the saturated Landauer equality $\\Delta S = k_B \\ln 2$ and the Bekenstein-Hawking law $S = k_B A/(4l_p^2)$, one obtains $\\Delta A = 4l_p^2 \\ln 2$ for the area decrease when the black hole loses one bit. Setting this equal to the area quantum of a single spin-$1/2$ puncture, $a(1/2) = 4\\pi l_p^2 \\gamma \\sqrt{3}$, yields $\\gamma_{\\rm Land} = \\ln 2/(\\pi\\sqrt{3})$, identical to the value from Eq. (7). Repeating the same identification for Barrow entropy gives $\\gamma_B = \\frac{\\ln 2}{\\pi\\sqrt{3}} \\frac{1}{1+\\Delta/2}\\left(\\frac{4l_p^2}{A}\\right)^{\\Delta/2}$, and for modified Kaniadakis entropy gives $\\gamma_{MKE} = \\frac{\\ln 2}{\\pi\\sqrt{3}}\\sqrt{1+\\kappa^2\\left(\\frac{A}{4l_p^2}\\right)^2}$; both reduce to the standard $\\gamma$ when $\\Delta\\to 0$ or $\\kappa\\to 0$. The paper interprets the resulting area dependence as an effective, model-dependent feature rather than a change in the true LQG parameter.","pith_inferences":["If the per-bit/per-puncture identification is taken literally, a black hole radiating $N$ bits should lose area in integer multiples of $a(1/2)$; observing a different area quantum would force the spin labelling or the saturated-equality assumption to change.","The same Landauer-based construction could be applied to other entropy proposals (Tsallis, R\\'enyi, loop-quantum-corrected logarithms), yielding a family of predicted effective $\\gamma$ values that could be compared against horizon-temperature or evaporation-time constraints.","The equality between the Landauer and Boltzmann-Gibbs derivations is not an accident in the paper's own reasoning: both count $2^N$ states, suggesting that the spin-$1/2$ puncture is itself a bit, though the paper does not develop this reading into an independent justification.","A testable extension would be to compute $\\gamma$ with a subleading spin $j>1/2$ or with a distribution of spins; if such corrections shift the predicted $\\gamma$ away from $\\ln 2/(\\pi\\sqrt3)$, the one-bit-one-puncture assumption would be falsifiable."],"forward_implications":["The Immirzi parameter is fixed by information thermodynamics alone, giving exactly $\\gamma = \\ln 2/(\\pi\\sqrt{3})$, in agreement with the value from Boltzmann-Gibbs microstate counting.","If both routes agree, the Landauer principle provides independent thermodynamic support for the standard value of the Immirzi parameter in Loop Quantum Gravity.","Under Barrow entropy the effective $\\gamma_B$ decreases with the fractal exponent $\\Delta$; under modified Kaniadakis entropy $\\gamma_{MKE}$ grows with $\\kappa$, with both tending to the standard value in the limiting cases.","Because the Barrow and Kaniadakis derivations make $\\gamma$ depend on the horizon area, those entropies should be regarded as effective thermodynamic descriptions; the underlying LQG parameter and geometric operators stay fixed.","Black hole evaporation that loses one bit at a time saturates Landauer's bound, so the information loss occurs with maximum thermodynamic efficiency."],"supporting_citations":[{"why":"Supplies the area spectrum formula $a(j)=8\\pi l_p^2\\gamma\\sqrt{j(j+1)}$ used to compute the spin-1/2 area quantum.","marker":"[2–6]"},{"why":"Provides the Boltzmann-Gibbs derivation of $\\gamma=\\ln2/(\\pi\\sqrt3)$ that the Landauer result is claimed to match exactly.","marker":"[7]"},{"why":"States the Landauer principle, the information-thermodynamics bound whose saturated form $\\Delta S=k_B\\ln2$ drives the derivation.","marker":"[8]"},{"why":"Defines Barrow entropy with fractal exponent $\\Delta$, the framework for the modified $\\gamma_B$ expression.","marker":"[21]"},{"why":"Introduces Kaniadakis $\\kappa$-statistics, the non-extensive entropy family used to build the modified Kaniadakis framework.","marker":"[31]"},{"why":"Proposes the modified Kaniadakis entropy for black holes, Eq. (28), whose variation yields $\\gamma_{MKE}$.","marker":"[42]"}],"fun_headline_variants":["Landauer principle yields Immirzi, no Gibbs count","One-bit erasure fixes gamma in loop gravity","Info thermodynamics derives Immirzi parameter","Alternative entropies modify Immirzi parameter"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole chain rests on identifying the erasure of one bit with the removal of exactly one spin-1/2 puncture, so that $\\Delta S=k_B\\ln2$ and $\\Delta A=a(1/2)$; if a bit erases several punctures, or the dominant puncture spin is not 1/2, or the saturated Landauer equality fails inside non-extensive entropies, every derived value of $\\gamma$ changes.","fun_headline_variants_meta":{"raw":{"variants":["Landauer principle yields Immirzi, no Gibbs count","One-bit erasure fixes gamma in loop gravity","Info thermodynamics derives Immirzi parameter","Alternative entropies modify Immirzi parameter"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000238,"raw_usage":{"total_tokens":1549,"prompt_tokens":1024,"completion_tokens":525,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":640,"completion_tokens_details":{"reasoning_tokens":466}},"tokens_in":640,"tokens_out":525,"duration_ms":4746,"temperature":1.0,"reasoning_tokens":466,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T12:25:52.416445+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure or compute the area change that accompanies a one-bit loss of information from a black hole horizon. If it is not $4l_p^2\\ln2$, for instance if it is a multiple of that or depends on the horizon area, then equating it to the single spin-1/2 puncture quantum $4\\pi l_p^2\\gamma\\sqrt3$ fails and the derived $\\gamma$ cannot be sustained. Within LQG itself, a calculation showing that macroscopic black hole entropy is dominated by punctures with $j>1/2$ would equally falsify the identification used here.","supporting_citations":[{"cited_title":"Dreyer, Phys","cited_arxiv_id":null,"evidence_quote":"Provides the Boltzmann-Gibbs derivation of $\\gamma=\\ln2/(\\pi\\sqrt3)$ that the Landauer result is claimed to match exactly."},{"cited_title":"Ashtekar, J","cited_arxiv_id":null,"evidence_quote":"States the Landauer principle, the information-thermodynamics bound whose saturated form $\\Delta S=k_B\\ln2$ drives the derivation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines Barrow entropy with fractal exponent $\\Delta$, the framework for the modified $\\gamma_B$ expression."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces Kaniadakis $\\kappa$-statistics, the non-extensive entropy family used to build the modified Kaniadakis framework."},{"cited_title":"Kaniadakis and A","cited_arxiv_id":null,"evidence_quote":"Proposes the modified Kaniadakis entropy for black holes, Eq. (28), whose variation yields $\\gamma_{MKE}$."}],"review_version":1}