{"id":"4654a404-c3b6-4081-8095-59b55493f513","arxiv_id":"2502.03603","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"One-shot classical capacities equal, up to error terms, the extractable work from correlations after transmission, yielding the equivalence n bits = n times kBT ln2 of transmitted energy.","lead":"This paper proves that one-shot classical communication capacities can be bounded by work extraction from correlations, giving a quantitative link between transmitting information and transmitting energy. The result is used to state a dynamical version of Landauer's principle and to give a thermodynamic reading of the Holevo-Schumacher-Westmoreland theorem.","discovery_kind":"unification","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Corollary 2's per-message claim does not follow from average success; the exact n-bit/n-energy equivalence is not proven as stated.","rationale":"The mathematical core, Theorems 1–4, appears technically sound and I do not contest it. The central advertised claim, however, is the exact equivalence in Corollaries 1 and 2 and the interpretation that work extracted from the output correlations is energy transmitted by the same physical process. Both rest on the unproven per-message reliability assertion: Fact 1's average success condition cannot yield Eq. (81). This is an internal proof gap, not a matter of convention. The standard expurgation repair changes the bit count from n to n−O(√ε), which is consistent with the earlier 'up to one-shot error terms' caveat but invalidates the unqualified Corollary. The reader's weakest_assumption about the operational identification of transmitted energy is related but distinct; I focus on the concrete logical gap in the derivation. The reader already conditioned acceptance on the exactness issues, and my concern supports that conditional posture, so the verdict remains CONDITIONAL with no change.","tokens_in":32585,"tokens_out":11369,"duration_ms":117596,"concrete_test":"Construct an explicit counterexample to Eq. (81) from average success: let M=4 and let Π_M(N) act as the identity on |0⟩,|1⟩,|2⟩ and send |3⟩ to |0⟩ with probability 1. The uniform average success is 3/4 = 1−ε with ε=1/4, so Fact 1 holds, but for m=3 the trace-norm distance is 1, not O(ε). Then run the Corollary 2 work-extraction calculation on the expurgated 3-symbol subcode consisting of the messages that are individually reliable: the extractable correlation work is log2 3 ≈ 1.585 bits of k_BT ln2, not n=2 bits. This demonstrates that the average-to-per-message step is where the exact constant n is lost, and that the corollary needs an explicit error-term reformulation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Corollary 2's proof asserts Eq. (81): for every m, ||Π_M(N)(|m⟩⟨m|)−|m⟩⟨m|||_1 = O(ε), citing Fact 1. Fact 1 only guarantees the uniform average success probability is at least 1−ε. Average success does not imply per-message success: a code can have a √ε fraction of messages fail with probability near 1 while the average error is still ε. Thus the observations that 'n bits are transmitted' and that Φ_MM′ is approximately preserved are not justified for every message; the trace-norm closeness in Eq. (82) also needs per-message control, not just average. A standard expurgation gives a subcode of size M(1−√ε) with per-message error O(√ε), reducing the bit count to n−O(√ε). Therefore the proof establishes at best n−O(√ε) bits accompanied by (n−O(√ε)) k_BT ln2 of extractable work, not the exact n stated in Corollaries 1 and 2. Since this same step grounds the claim that W_corr is energy transmitted by the physical process Π_M(N), the advertised dynamical Landauer principle is not yet proven at the stated precision.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes a one-shot thermodynamic characterization of classical communication through quantum channels. It defines Θ-assisted classical capacities, proves entropic bounds (Theorems 1 and 2), introduces correlation-based work-extraction quantities as energy transmission tasks (Section IV), and shows that these bound the capacity up to one-shot error terms (Theorem 4). The authors interpret this as a dynamical Landauer principle, namely that transmitting n bits is accompanied by transmitting n k_B T ln 2 of work-like energy, and they derive the HSW theorem plus strong-converse/no-go statements in the asymptotic limit (Proposition 1, Corollaries 3 and 4). The technical proofs are detailed and follow standard one-shot information-theoretic techniques.","tokens_in":32755,"tokens_out":13240,"duration_ms":120998,"significance":"If the central equivalence survives the concerns below, the paper provides a quantitative bridge between classical information transmission and work extraction from correlations, and it gives an interesting thermodynamic reading of the HSW theorem. The proofs of Theorems 1, 2, and 4 are thorough and generally sound at the level of standard one-shot capacity bounds; the asymptotic results and strong-converse statements are nontrivial and go beyond a simple restatement of known capacity formulas. The main caveats are that the strongest advertised corollary relies on a per-message guarantee that is not implied by the average-success definition, and that the \"energy transmitted\" figure of merit is constructed from the same entropic quantities used in the capacity bound, so the physical content of the equivalence depends on accepting that operational definition.","major_comments":[{"comment":"Fact 1 (Eq. (7)) defines the capacity via the average success probability over uniformly distributed messages. The proof of Corollary 2 asserts, for every m, that ∥Π_M(N)(|m⟩⟨m|)−|m⟩⟨m|∥_1 = O(ε), and then derives Eq. (82) from this per-message statement. This does not follow from average success: a code can have a √ε fraction of messages failing with probability close to 1 while the average error is still ε. A standard expurgation gives a subcode of size M(1−√ε) with per-message error O(√ε), so the proof establishes at best n−O(√ε) bits accompanied by (n−O(√ε)) k_B T ln 2 of extractable work, not the exact n stated in Corollaries 1 and 2. The advertised dynamical Landauer principle therefore needs either an expurgation step or a restatement of the corollaries at the corrected precision.","section":"§V B, Eqs. (81)–(82)"},{"comment":"The quantity W^ε_{Φ|Θ,(1)} is defined using the same maximally correlated state Φ_MM′, the same trace-norm constraint ∥Π_M(N)(I/M)−I/M∥_1<2ε, and the same smoothed Rényi 0-entropy D^ε_0 that appears in Theorem 1's capacity upper bound. Via Åberg's Theorem 3, the upper bound in Theorem 4 is therefore a direct translation of Theorem 1's bound into work units. The physical claim that this quantity represents \"genuinely transmitted energy\" rests on the stipulation in Section IV C that transmitted energy should be identified with extractable work from the output bipartite correlation under fully degenerate Hamiltonians. This is an internally consistent operational definition, but it is not derived from or compared with a pre-existing notion of energy transmission, and the one-shot equivalence between W_corr and W_Φ themselves is asserted rather than proved. The paper should either justify this identification more explicitly or qualify the claim that information and energy transmission are equivalent.","section":"§IV C, Eqs. (74)–(76); Theorem 4"}],"minor_comments":[{"comment":"The statement 'The ability to transmit n bits of information is equivalent to the ability to transmit n×(k_B T ln 2) energy' drops the one-shot error terms that appear in Theorem 4; please state the ε-dependence explicitly or add 'up to one-shot error terms' in the corollary statement.","section":"Corollary 1"},{"comment":"The inequality as printed, C^ε_{(1)|θ-equi}(N^{⊗k}) ≤ C^{3ε}_{(1)}(N)+O(log ε), is dimensionally inconsistent because the right-hand side does not depend on k; presumably it should be C^{3ε}_{(1)}(N^{⊗k}).","section":"§V C, Eq. (105)"},{"comment":"The text reads 'Hovelo information'; this should be 'Holevo information'.","section":"§V C, before Eq. (86)"},{"comment":"The placement of the trace-norm constraint inside the supremum is hard to parse; a displayed constraint set would improve readability.","section":"Theorem 1, Eq. (21)"},{"comment":"The data-processing inequality for D^ε_0 via Fact 6 requires ε to be no larger than the minimal positive eigenvalues of the relevant states; Eq. (72) states this only as 'for a small enough ε' and would benefit from stating the condition explicitly.","section":"§IV C, Eq. (72)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a companion to a PRL by the same author, and the referee did not have that PRL. The added technical value here appears to be in the detailed proofs and the asymptotic propositions; the editor may wish to confirm that the arXiv version is not merely a duplication of the PRL's supplementary material. The main fix required before acceptance is the per-message versus average-success gap in Corollary 2."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nQuick take: the one-shot bounds are real; the dynamical Landauer equivalence is not proven at the advertised precision. The stress-test note is right that Corollary 2's per-message claim does not follow from average success, and the exact n-bit / n·k_BT·ln2 statements drop error terms that the theorems actually produce.\n\nWhat is genuinely new: Theorems 1 and 2 give Theta-assisted one-shot classical capacity bounds generalizing Wang-Renner, with detailed Hayashi-Nagaoka and Stein arguments. Theorem 4's connection between these capacities and work extraction from correlations is a real bridge result, and the asymptotic HSW-with-thermodynamic-constraints package (Proposition 1, Corollaries 3 and 4) is a nice way to express the no-go result that generating informational non-equilibrium does not enhance asymptotic classical communication. The paper is careful with the one-shot framework and the proofs are mostly step-by-step.\n\nSoft spots, in proportion. Corollary 2 is the main one. Equation (81) asserts per-message trace-norm closeness for every m, but Fact 1 only gives average success; average success does not bound per-message failure without an expurgation step. The standard expurgation reduces the code to M(1−√ε) messages with per-message error O(√ε), so you get n−O(√ε) bits, not n. Equation (82) has the same per-message problem. This is fixable, but it means the claim that transmitting n bits must be accompanied by exactly n·k_BT·ln2 of transmitted energy is not established. Corollary 1 as written is similarly too strong: the theorems have one-shot error terms, and the exact equality should carry an 'up to O(ε)' caveat.\n\nSecond soft spot: the figure of merit W_Φ in Eq. (76) is constructed from the same smoothed relative Rényi 0-entropy that bounds the capacity, so Theorem 4's upper bound is partly a restatement of Theorem 1 in work units. That does not make it wrong, but it shifts the physical content onto the operational definition in Section IV C: 'genuinely transmitted energy' is extractable work from output correlations under fully degenerate Hamiltonians and diagonal states. If that identification does not match what one means by energy transmitted through a channel, the advertised equivalence is narrower than the abstract suggests. The paper states the setup but does not argue for its necessity.\n\nOverall: the mathematical core is sound and the one-shot bounds are worth having. The advertised Landauer principle needs revision of Corollaries 1–2 and a clear restatement with expurgation and error terms. I would send this to a serious referee, conditionally—the fixes are standard but not cosmetic.\n\nRecommendation: engage with it. Assign a referee comfortable with one-shot information theory and thermodynamics, and ask specifically whether the per-message step can be repaired. The paper deserves referee time; it just should not be published with Corollaries 1–2 as stated.","headline":"Solid one-shot capacity bounds, but the advertised exact n-bit/energy equivalence rests on an unjustified per-message step and dropped error terms.","tokens_in":33336,"tokens_out":2935,"would_cite":true,"duration_ms":28912,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P45","94A40"],"pacs":[],"model":"deepseek-v4-flash","headline":"Transmitting n bits of classical information is equivalent to transmitting n×k_BT ln2 of work-like energy.","keywords":["quantum channel capacity","one-shot classical capacity","Landauer's principle","quantum thermodynamics","work extraction","informational non-equilibrium","Holevo-Schumacher-Westmoreland theorem","classical communication"],"falsifier":"One could refute the equivalence by exhibiting a channel that transmits $n$ bits of classical information one-shot but whose physically transmitted energy, measured by a direct accounting of energy changes in sender and receiver with non-degenerate Hamiltonians or coherent inputs, is strictly below $n\\times k_BT\\ln2$; the paper's energy-transmission definition would then miss an aspect of real energy transfer.","tokens_in":32315,"feed_emoji":"⚡","tokens_out":9078,"duration_ms":76505,"temperature":0.7,"pith_summary":"This paper tries to prove a quantitative equivalence between transmitting classical information and transmitting energy through a quantum channel. The central result bounds every one-shot classical capacity between two energy-transmission figures of merit, so that sending $n$ bits of classical information is equivalent, up to one-shot error terms, to transmitting $n\\times k_BT\\ln 2$ of work-like energy. The author calls this a dynamical version of Landauer's principle because it concerns transmitting information rather than erasing it. In the asymptotic limit, the same bounds reproduce the Holevo-Schumacher-Westmoreland theorem and imply strong-converse statements about generating informational non-equilibrium. A reader should care because the result gives a concrete, quantitative sense in which communication and thermodynamics are the same task.","feed_headline":"n bits of info equals n×k_BT ln2 of transmitted energy","feed_subtitle":"A new theorem ties one-shot channel capacity to extractable work, extending Landauer from erasure to transmission.","key_machinery":"The central object is the one-shot energy transmission task, whose figure of merit is the extractable work from the receiver's output bipartite correlation, $W^{\\epsilon}_{\\mathrm{corr}|\\Theta,(1)}(\\mathcal{N})$ (and its simplified version $W^{\\epsilon}_{\\Phi|\\Theta,(1)}(\\mathcal{N})$). The machinery converts the smoothed relative Rényi $0$-entropy $D^{\\epsilon}_0$ into units of $k_BT\\ln2$ via a one-shot work-extraction theorem, and uses the hypothesis-testing relative entropy $D^{\\epsilon}_h$ to bound the classical capacity. Because $D^{\\epsilon}_0$ measures both correlation maintenance and extractable work, it is the bridge that makes the two tasks coincide.","core_discovery":"The paper's central claim is that one-shot classical information transmission and one-shot work-like energy transmission are the same task up to error terms. The precise statement is Theorem 4: for a set of superchannels $\\Theta$, a channel $\\mathcal{N}$, and errors $0<\\delta\\le\\omega<\\epsilon\\le 1-1/\\sqrt{2}$, the capacity satisfies $$$W^{{\\omega}}$_{\\mathrm{corr}|\\Theta,(1)}(\\mathcal{N}) - k_BT \\ln\\frac{4\\epsilon}{(\\epsilon-\\omega)^2(1-\\omega)} \\le (k_BT \\ln 2) $C^{{\\epsilon}}$_{\\Theta,(1)}(\\mathcal{N}) \\le $W^{{\\epsilon+\\delta}}$_{\\Phi|\\Theta,(1)}(\\mathcal{N}).$$ Corollary 1 phrases this as the equivalence between transmitting $n$ bits and transmitting $n\\times k_BT\\ln2$ energy. The paper then argues that this equivalence is genuinely dynamical: in an explicit multi-trial protocol the same channel operation transmits the information and the work-like energy simultaneously, which it calls a dynamical Landauer principle.","pith_inferences":["If the equivalence is taken physically, a systematic mismatch between correlation-extractable work and direct energy accounting in an experiment would force a revision of the definition of transmitted energy, not just of the theorem.","A natural extension would be to ask whether sending quantum information, such as entanglement or quantum messages, also implies the same per-bit work-like energy transmission; the paper only states the classical case.","The one-shot formulation means the equivalence is not just an asymptotic statement, so it could be probed in few-qubit devices where finite-size error terms are non-negligible."],"forward_implications":["A channel's one-shot classical capacity can be bounded from above and below by how much work-like energy it can transmit, so energy-transmission experiments become capacity witnesses.","Landauer's principle acquires a dynamical counterpart: erasing a bit costs at least $k_BT\\ln2$, and transmitting $n$ bits must carry at least $n\\times k_BT\\ln2$ of work-like energy with it.","In the asymptotic limit the bounds reproduce the HSW theorem, giving that theorem a thermodynamic interpretation.","Strong-converse and no-go results follow: allowing encoders and decoders to generate informational non-equilibrium cannot increase the asymptotic classical capacity."],"supporting_citations":[{"why":"Supplies the one-shot work-extraction theorem used to convert $D^{\\epsilon}_0$ into extractable work in Eq. (70).","marker":"[15]"},{"why":"Supplies the one-shot classical capacity bounds and hypothesis-testing relative entropy that Theorems 1 and 2 tighten and generalise.","marker":"[16]"},{"why":"Landauer's erasure principle is the static statement whose dynamical counterpart the paper derives.","marker":"[17]"},{"why":"The HSW theorem is the asymptotic result that the paper reproduces and gives a thermodynamic interpretation.","marker":"[18–20]"},{"why":"Defines min-relative entropy, which relates to $D^{\\epsilon}_0$ and underpins its data-processing and continuity properties.","marker":"[30]"},{"why":"Provides the matrix inequality that underlies the lower-bound proof of the one-shot capacity bound.","marker":"[31]"},{"why":"Shows how to quantify extractable work from correlations, the basis of the energy transmission tasks.","marker":"[32]"}],"fun_headline_variants":["Transmitting info = transmitting energy at k_BT ln2 per bit","Landauer's principle now covers info transmission, not just erasure","One-shot info capacity tied to work transmission exactly","k_BT ln2 per bit: the energy cost of sending information","Dynamical Landauer: sending info and energy are the same task"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that 'genuinely transmitted energy' is correctly quantified by the work extractable from the receiver's output bipartite correlation under fully degenerate Hamiltonians and energy-incoherent states; the paper states this identification in Section IV C rather than deriving it from a more direct definition of energy transmitted by a channel.","fun_headline_variants_meta":{"raw":{"variants":["Transmitting info = transmitting energy at k_BT ln2 per bit","Landauer's principle now covers info transmission, not just erasure","One-shot info capacity tied to work transmission exactly","k_BT ln2 per bit: the energy cost of sending information","Dynamical Landauer: sending info and energy are the same task"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000311,"raw_usage":{"total_tokens":1758,"prompt_tokens":920,"completion_tokens":838,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":536,"completion_tokens_details":{"reasoning_tokens":748}},"tokens_in":536,"tokens_out":838,"duration_ms":7251,"temperature":1.0,"reasoning_tokens":748,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T04:22:15.042480+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"One could refute the equivalence by exhibiting a channel that transmits $n$ bits of classical information one-shot but whose physically transmitted energy, measured by a direct accounting of energy changes in sender and receiver with non-degenerate Hamiltonians or coherent inputs, is strictly below $n\\times k_BT\\ln2$; the paper's energy-transmission definition would then miss an aspect of real energy transfer.","supporting_citations":[{"cited_title":"Faist, F","cited_arxiv_id":null,"evidence_quote":"Supplies the one-shot classical capacity bounds and hypothesis-testing relative entropy that Theorems 1 and 2 tighten and generalise."},{"cited_title":"Faist and R","cited_arxiv_id":null,"evidence_quote":"Landauer's erasure principle is the static statement whose dynamical counterpart the paper derives."},{"cited_title":"Lostaglio, An introductory review of the resource theory approach to thermodynamics, Rep","cited_arxiv_id":null,"evidence_quote":"Defines min-relative entropy, which relates to $D^{\\epsilon}_0$ and underpins its data-processing and continuity properties."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows how to quantify extractable work from correlations, the basis of the energy transmission tasks."}],"review_version":1}