{"id":"b56601ab-f626-4229-961a-c6a7f33129aa","arxiv_id":"2412.04297","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"The energy of a single dissipative soliton is limited by a thermodynamic instability: rising entropy and a transition to negative temperature favor breakup into multiple lower-energy pulses.","lead":"This paper uses a thermodynamic analogy to explain why dissipative solitons in mode-locked lasers cannot store unlimited energy: entropy growth and a transition to a negative-temperature phase push the soliton to split into multiple lower-energy pulses. If correct, it gives laser designers a quantitative criterion for the maximum pulse energy of chirped-pulse oscillators and fiber lasers.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The negative-temperature breakup is asserted, not demonstrated: Eq. D3's entropy re-scaling is ad hoc and the paper itself reports no spontaneous decay of sustained single pulses, so E*≈20/40 may be a self-start statistic rather than an instability threshold.","rationale":"The single most load-bearing step is not the spectral ansatz itself but the leap from a negative scalar derivative to a dynamical instability. The reader's weakest-assumption is upstream and correct; however, even a reader who accepts the entropy convention and the spectral-probability interpretation cannot find a proof that Theta<0 makes the DS split. The paper's own caveat that sustained single-pulse regimes show no spontaneous decay is direct, in-manuscript evidence against the strong reading of the claim. If the proposed simulation fails to show splitting, the manuscript should be revised to claim that thermodynamic variables correlate with multi-pulse self-starting from noise, not that negative temperature causes breakup; the energy-scalability limits would then be probabilistic rather than thermodynamic-instability bounds. The conditional verdict remains appropriate because the central claim can be rescued by a deterministic splitting test but is currently insufficiently supported.","tokens_in":19453,"tokens_out":6295,"duration_ms":63374,"concrete_test":"Run deterministic simulations of Eq. (1) in the DSR region, starting from the analytic single-P+ field profile (inverse Fourier transform of Eq. A12) at E* just above the Theta=0 onset (approximately 20) and above the Delta Hs crossover (approximately 40), with weak additive noise and the same parameters as Figs. 1 and 2. Integrate for many cavity round trips and record whether the single pulse spontaneously splits into two or more P- pulses. If no split occurs in the sustained regime, the 'negative-temperature instability' is not a dynamical instability and the predicted breakup thresholds are not physical; if it splits near the predicted E*, the thermodynamic mechanism is directly supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The center of the claim is Section III E: when Theta becomes negative, the single P+ DS becomes 'overheated' and unstable, so it splits into multiple P- pulses. This causal step is not established. First, the temperature is computed from Hs after dropping the normalization term in the Shannon entropy H of Eq. (D2); that ad hoc re-scaling in Eq. (D3) makes Hs a function only of Delta/Xi, so the sign of Theta is not an invariant thermodynamic property but a property of the chosen entropy convention. Second, even granting the spectral-probability ansatz of Section III B, partial Hs / partial U < 0 is not a linear-stability criterion for the strongly dissipative, non-equilibrium Eq. (1). The paper itself concedes in Section IV that 'spontaneous transitions or decay are not seen when the regime is sustained' and that multipulsing appears during the initial noise-driven formation stage; Appendix D also disavows free-energy minimization as a dynamic stability criterion. Thus the numerical evidence in Fig. 5 supports a noise-selected multi-pulse outcome, not the disintegration of an established single soliton at E* approximately 20 or E* approximately 40.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a thermodynamic description of strongly chirped dissipative solitons governed by the complex cubic-quintic Ginzburg-Landau equation. Starting from the adiabatic truncated-Lorentzian spectral ansatz (Eq. 2), the authors define an entropy Hs, internal energy U, and temperature Θ (Eqs. 8-10, Appendix D) and use these to argue that energy scalability in the dissipative-soliton-resonance (DSR) regime is limited by an entropy increase and by a transition to negative temperature at dimensionless energy E*≈20, which drives breakup into multiple lower-energy P-0 solitons. The paper also reports numerical simulations of noise-driven pulse formation and experimental spectra from a Cr2+:ZnS chirped-pulse oscillator, claiming qualitative agreement with the predicted DSR signatures: a growing central Lorentzian spike, saturation of spectral broadening, and pulse stretching.","tokens_in":19778,"tokens_out":6006,"duration_ms":61407,"significance":"If the thermodynamic interpretation were rigorously established, the paper would provide a practical design rule for the maximum single-pulse energy in chirped-pulse oscillators and all-normal-dispersion fiber lasers. The manuscript's strengths are its systematic adiabatic derivation of the DS spectrum and master diagram (Appendix A, Fig. 1), the clear identification of the P+0/P-0 branches and their distinct energy-scaling behavior, the explicit numerical noise-seeded self-start statistics (Fig. 5), and the availability of commented Mathematica code for the thermodynamic quantities. The experimental spectra (Fig. 2) do show the expected Lorentzian spike and spectral saturation. However, the central negative-temperature instability and the quantitative thresholds E*≈20 and E*≈40 are not currently supported: they depend on an ad hoc entropy rescaling, an unspecified thermodynamic path, and a conjectural mapping from the spectral ansatz to a probability distribution, while the paper itself reports no spontaneous decay of sustained single pulses. The quantitative claims therefore require substantial revision before the paper can be accepted.","major_comments":[{"comment":"The entropy Hs used to compute the temperature is obtained from the full Shannon entropy H in Eq. (D2) by dropping the term ln(2Ξ tan^-1(Δ/Ξ)). This term is not a constant: it depends on Ξ and Δ, and therefore on U through Eq. (D4). Consequently ∂Hs/∂U differs from ∂H/∂U by the derivative of a state-dependent quantity, so the sign of the resulting temperature is a property of the chosen entropy convention rather than an invariant thermodynamic prediction. The paper provides no argument that the omitted term is thermodynamically irrelevant; it is dropped merely to make Hs positive and finite as Ξ→0. Since the negative-temperature threshold E*≈20 in Fig. 11 and the 'overheated' instability claim in Section III E are the central conclusions of the paper, the temperature should be recomputed with the full H, or the rescaling must be justified physically. As it stands, the negative-temperature result may be an artifact of the rescaling.","section":"Section III E and Appendix D, Eq. (D3)"},{"comment":"The causal link between negative Θ and pulse splitting is not demonstrated. Section IV states that 'spontaneous transitions or decay are not seen when the regime is sustained. Such transitions appear during the initial stage of DS formation.' Figure 5 presents statistics from 150 stochastic samples of noise-driven formation, showing that multipulsing becomes more probable at higher E*_cw. This supports a noise-selected outcome during self-start, not the disintegration of an established single P+0 DS when Θ crosses zero. To substantiate the breakup claim, the authors should either simulate a sustained single-pulse initial condition perturbed above the predicted threshold, or explicitly restrict the claim to self-start statistics. As written, the assertion in Section III E that an 'overheated' DS 'tends to relax' into multiple pulses is unsupported by the numerical evidence presented.","section":"Section IV and Fig. 5"},{"comment":"The interpretation of the DS spectrum p(ω) as a normalized probability distribution of quasi-particle microstates is a conjecture that is not independently tested. The three DSR 'signatures' (Lorentzian spike, spectral saturation, pulse stretching) are direct consequences of the truncated-Lorentzian ansatz Eq. (2) and the definitions of Ξ and Δ, so their observation in Fig. 2 does not validate the thermodynamic interpretation. The negative temperature and the entropy-preference threshold E*≈40 are derived from this spectral-probability mapping and therefore inherit its assumptions. The manuscript should explicitly identify which predictions are robust to abandoning the quasi-particle interpretation, or provide an independent test—for example, connecting Hs to the measured multipulsing statistics via fluctuation relations. The caveats in footnote 1 and Appendix D ('the analogy to thermodynamics is not literal', 'free energy minimization cannot be considered a criterion of dynamic stability') should be reflected in the abstract's claims.","section":"Section III B and Appendix D, Eqs. (D1)-(D4)"},{"comment":"The definition Θ = (∂Hs/∂U)^{-1} does not specify which variables are held fixed in the derivative. Hs and U are functions of both Ξ and Δ (Eqs. D3-D4), and along the DS branch these are not independent (Eqs. A6-A8). Without specifying the thermodynamic path—for example, constant C and Σ, or constant Δ—the temperature is not uniquely defined, and the Θ=0 crossing may depend on that choice. The authors should state the constraints used to generate Figs. 10 and 11 and verify that the negative-temperature onset is independent of the path chosen.","section":"Eq. (10) and Fig. 11"}],"minor_comments":[{"comment":"The section title 'DS \"quantization\" and thermolization' contains a typo: 'thermolization' should be 'thermalization'.","section":"Section III C"},{"comment":"Section IV states that the entropy difference becomes positive at E*≈30, whereas Fig. 9(a) and the surrounding text state E*≈40. These numbers should be reconciled.","section":"Section IV vs. Fig. 9(a)"},{"comment":"The caption says 'Percentage of multiple DSs' but does not define whether this is the fraction of samples with more than one pulse, the average pulse number, or another quantity; the y-axis label should be specified.","section":"Fig. 5 caption"},{"comment":"In Eq. (5), the argument of the sinc function is Δ(τ-t), which is dimensionless only if Δ is understood as an angular frequency; please state the convention used for spectral half-widths.","section":"Eq. (5)"},{"comment":"The abbreviation 'CPO' is used both for 'chirped-pulse oscillator' and in the compound 'CPO-CPA'; please define it at first use and keep the usage consistent.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a question of practical importance for high-energy femtosecond lasers and contains a substantial analytical apparatus plus reproducible code, which is commendable. However, the central negative-temperature claim is not yet defensible because of the entropy rescaling and the absence of direct evidence for breakup of sustained pulses. I would encourage the editor to request a revision that either strengthens the thermodynamic derivation (e.g., by using the full Shannon entropy and specifying the thermodynamic path) or reframes the paper's contribution as a phenomenological, noise-selected multipulsing threshold rather than a thermodynamic instability. If the authors can show that the negative-temperature onset is independent of the entropy convention, the paper would be a strong candidate for acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read it. The genuinely new piece is the claim that energy scalability of dissipative solitons is capped by a thermodynamic transition: entropy grows with energy, internal energy eventually decreases, temperature goes negative, and the single-pulse state becomes unstable around E*~20–40. That specific quantitative threshold is not in their earlier papers, and it is a useful, falsifiable target. The paper also ships commented Mathematica code and shows real Cr:ZnS CPO spectra, which is more than most theory papers. The adiabatic spectrum and DSR machinery are largely self-borrowed, but that is legitimate; the control-parameter diagram is a solid framework.\n\nThe soft spots are in the load-bearing step. First, the negative-temperature result rests on an entropy rescaling in Appendix D: they start with Shannon entropy H for the normalized spectral distribution (D2), then drop the normalization term to get Hs (D3). Sign is convention-dependent; a different shift changes the sign of dHs/dU and the location of the Θ=0 crossing. You cannot drop the constant from one side and keep it in the other and call the result physical. They do not test robustness to that choice.\n\nSecond, the thermodynamics analogy is explicitly non-literal, and they concede in Section IV that sustained single pulses do not spontaneously decay; multipulsing appears during noise-driven formation. That means the simulations support a noise-selected multi-pulse outcome, not the disintegration of an established soliton at E*≈20 or 40. The abstract and conclusions state the causal claim more strongly than the evidence. The free-energy minimization disavowal in Appendix D sits awkwardly with the Maxwell-point wording in the text.\n\nThird, the experimental comparison is qualitative and partly circular: the DSR signatures (Lorentzian spike, spectral saturation, stretching) are properties of the ansatz, so agreement with those signatures confirms the model but not the thermodynamic instability.\n\nThe stress-test was mostly right. The central causal step—negative temperature causes breakup—is asserted, not shown. The paper is still coherent and honest; it flags several of its own limitations. The citation pattern is heavy on the group's prior work because it is developing its own framework; no red flag there.\n\nWho is this for: people designing chirped-pulse oscillators and all-normal-dispersion fiber lasers who want a rule of thumb for energy ceilings, and theorists interested in thermodynamic analogies in CGLE systems. It deserves a serious referee—the analytic machinery is nontrivial and the topic is timely—but only with a referee who asks for a linear-stability analysis or a rewritten claim that separates heuristic thermodynamic language from what the numerics actually establish. I would not cite the specific E* thresholds in my own work yet.","headline":"The paper has a genuinely new quantitative claim—dissipative-soliton energy ceilings set by negative temperature around E*≈20–40—but the causal step is not demonstrated, and the paper itself concedes the evidence points to noise-selected multipulsing rather than spontaneous breakup of a sustained pulse.","tokens_in":20249,"tokens_out":3003,"would_cite":false,"duration_ms":34205,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["42.65.Tg","42.60.Fc"],"model":"deepseek-v4-flash","headline":"The paper claims that energy scaling of a single dissipative soliton is capped by a negative-temperature instability that splits it into multiple pulses.","keywords":["dissipative soliton","dissipative soliton resonance","soliton thermodynamics","negative temperature","complex Ginzburg-Landau equation","chirped-pulse oscillator","all-normal-dispersion fiber laser","mode-locking"],"falsifier":"The claim would be falsified by a statistical self-start experiment: run many noise-seeded starts of the same chirped-pulse oscillator at a series of pump energies and record the number of pulses that emerge. The theory predicts that single-pulse probability drops below about 95% as the dimensionless energy $E^{*}$ passes roughly 20 and that multipulse states become entropically preferred past roughly 40; if single-pulse output remains the rule well beyond those thresholds, the thermodynamic instability is not the limiting mechanism. As a spectral check, the DSR spectrum must show a Lorentzian central spike of width $\\Xi$ shrinking toward zero while the cutoff $\\Delta$ saturates; a spectrum that keeps broadening without a narrowing spike contradicts the probability-distribution assumption underlying the negative temperature.","tokens_in":19272,"feed_emoji":"🌡️","tokens_out":12378,"duration_ms":116180,"temperature":0.7,"pith_summary":"This paper argues that a single dissipative soliton—the self-stabilizing pulse that mode-locked lasers emit—has a hard energy ceiling set by its own thermodynamics, not just by the stability of the laser equations. Working in the adiabatic theory of strongly chirped pulses, the authors treat the soliton's truncated Lorentzian spectrum as a probability distribution of quasi-particle microstates and derive an entropy and an effective temperature for the pulse. As energy grows, the two internal correlation scales decouple, the entropy rises, and past a threshold the internal energy starts to fall, so the effective temperature becomes negative; a negative-temperature single-pulse state is 'overheated' and unstable, and the system relaxes by splitting into several lower-energy pulses. The paper identifies the onset of negative temperature near $E^{*}\\approx 20$ and the entropy preference for multipulse complexes near $E^{*}\\approx 40$, and it reports qualitative agreement with measured spectra from a Cr$^{2+}$:ZnS chirped-pulse oscillator. If true, this gives laser designers a quantitative rule: below those thresholds single-pulse energy can grow safely, beyond them multipulsing is thermodynamically inevitable.","feed_headline":"Negative temperature caps the energy of a single laser pulse","feed_subtitle":"Beyond that point the pulse is 'overheated' and splits, so high-energy laser design must respect a thermodynamic limit.","key_machinery":"The carrying object is the truncated Lorentzian spectral profile $p(\\omega)\\propto (\\Xi^2+\\omega^2)^{-1}H(\\Delta^2-\\omega^2)$, interpreted as a normalized probability distribution of soliton quasi-particle microstates. It defines two correlation scales: the short 'graining' scale $l=\\pi/\\Delta$ and the long 'confining' scale $\\Lambda=1/\\Xi$. The entropy $H_s$ (Eq. 8 with the renormalization in Eq. D3), internal energy $U$ (Eq. 9/D4), and temperature $\\Theta=(\\partial H_s/\\partial U)^{-1}$ are all derived from this distribution, so the ratio $\\Xi/\\Delta$ controls the number of microstates. The mechanism that drives the claimed limit is the decoupling of $l$ and $\\Lambda$: in dissipative soliton resonance, $\\Xi\\to0$ while $\\Delta$ saturates, which raises the entropy; when $U$ simultaneously stops rising and begins to fall, the temperature goes negative and the single pulse becomes unstable against splitting into multiple $P_0^-$ pulses.","core_discovery":"On the paper's own terms, the discovery is that dissipative soliton resonance does not lead to unlimited energy accumulation: the same spectral condensation that lets a strongly chirped pulse stretch and store more energy also creates the instability that ends it. The soliton spectrum is a Lorentzian of width $\\Xi$ cut off at $\\Delta$ (Eq. 2), and the paper reads it as a Rayleigh-Jeans distribution of quasi-particle microstates. From this distribution it computes an entropy $H_s$ and an internal energy $U$; with increasing dimensionless energy $E^{*}$, $\\Xi$ shrinks toward zero while $\\Delta$ saturates, so the ratio of the confining scale $\\Lambda=1/\\Xi$ to the graining scale $l=\\pi/\\Delta$ grows and the entropy rises. At the point where $U$ begins to decrease with $E^{*}$, the reciprocal temperature $\\Theta^{-1}=\\partial H_s/\\partial U$ becomes negative. The single-pulse $P_0^+$ solution then is only metastable, and the system 'thermalizes' into a set of lower-energy $P_0^-$ pulses; the paper locates the negative-temperature onset near $E^{*}\\approx20$ and the entropy-preference crossover near $E^{*}\\approx40$, and it connects these thresholds to the experimentally observed multipulsing and spectral signatures in a Cr$^{2+}$:ZnS chirped-pulse oscillator.","pith_inferences":["Inference: because the breakup mechanism depends only on the truncated-Lorentzian spectral structure and the decoupling of the two correlation scales, the same negative-temperature threshold near $E^{*}\\approx20$ should appear in all-normal-dispersion fiber lasers and other strongly chirped soliton lasers, not only in solid-state chirped-pulse oscillators.","Inference: if the effective temperature is a genuine control parameter, reshaping the spectral dissipation profile—rather than lowering the pump energy—is a testable way to 'cool' the soliton ensemble and shift multipulsing to higher energies.","Inference: the entropy definition in Eq. (D3) is renormalized by an additive shift to remove an infinity as $\\Xi\\to0$, so the precise values $E^{*}\\approx20$ and $E^{*}\\approx40$ should be read as crossover locations; the robust content of the paper is the existence of an entropy-driven multipulsing transition, not the exact numbers."],"forward_implications":["A single dissipative soliton is thermodynamically safe only below the negative-temperature onset near $E^{*}\\approx20$; designs that push past this point should expect multipulsing to become increasingly probable.","Above $E^{*}\\approx40$, a complex of two or more equal $P_0^-$ pulses has higher entropy than a single $P_0^+$ pulse of the same total energy, so energy added to the laser goes into more pulses rather than a stronger single pulse.","The same three spectral signatures—growth of a Lorentzian central spike, saturation of the spectral half-width $\\Delta$, and asymptotic temporal stretching—mark both the entry into dissipative soliton resonance and the approach to the breakup limit, which is what makes the threshold observable.","The fidelity condition $\\Xi=\\Delta$ coincides with the best compressibility of the chirped pulse; beyond it the spectral chirp becomes strongly frequency-dependent and compression quality degrades, so operating near the fidelity curve optimizes both energy and pulse quality.","Near the breakup threshold the probability distribution over pulse number broadens and shifts to higher $n$, meaning the laser shows hysteresis and multistability: the same pump conditions can sustain a single pulse or several pulses depending on history."],"supporting_citations":[{"why":"Supplies the adiabatic solution of the Ginzburg-Landau equation that yields the truncated Lorentzian spectral profile in Eq. (2).","marker":"[39]"},{"why":"Establishes the master diagram, the fidelity curve, and the dissipative-soliton-resonance parametric space used throughout.","marker":"[40]"},{"why":"Provides the experimental Cr2+:ZnS chirped-pulse oscillator spectra and energy-scaling data that the theory is compared with.","marker":"[37]"},{"why":"Defines dissipative soliton resonance as the infinite-energy asymptotic that the paper's energy-scaling analysis extends.","marker":"[19]"},{"why":"Gives the kinetic-theory description of incoherent solitons that justifies treating the chirped pulse as a statistical ensemble of quasi-particles.","marker":"[23]"},{"why":"Supplies the thermodynamic theory of mode-locking self-start, including the noise-temperature interpretation used for the continuous-wave energy variable.","marker":"[31]"},{"why":"Provides the quantum-noise numerical simulations used for the multipulsing probability statistics in Fig. 5.","marker":"[44]"},{"why":"Defines the optical-soliton thermodynamic quantities (entropy and internal energy) on which Eqs. (8)-(10) are based.","marker":"[57]"}],"fun_headline_variants":["Negative temperature sets ceiling on soliton pulse energy","Laser pulse energy capped by negative temperature","Dissipative solitons hit energy limit via negative temperature","Soliton energy growth stops at negative temperature","Pulse splitting at negative temperature limits soliton energy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument stands on treating the soliton's truncated Lorentzian spectrum as a physical probability distribution of quasi-particle microstates, so the entropy and temperature derived from it are real; the paper itself notes the laser is far from equilibrium and the thermodynamic analogy is not literal, so if that spectral-probability reading fails, the negative temperature and the $E^{*}\\approx20$ and $E^{*}\\approx40$ thresholds are formal artifacts rather than a physical ceiling.","fun_headline_variants_meta":{"raw":{"variants":["Negative temperature sets ceiling on soliton pulse energy","Laser pulse energy capped by negative temperature","Dissipative solitons hit energy limit via negative temperature","Soliton energy growth stops at negative temperature","Pulse splitting at negative temperature limits soliton energy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000221,"raw_usage":{"total_tokens":1511,"prompt_tokens":1069,"completion_tokens":442,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":685,"completion_tokens_details":{"reasoning_tokens":368}},"tokens_in":685,"tokens_out":442,"duration_ms":4779,"temperature":1.0,"reasoning_tokens":368,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T21:33:24.384162+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"The claim would be falsified by a statistical self-start experiment: run many noise-seeded starts of the same chirped-pulse oscillator at a series of pump energies and record the number of pulses that emerge. The theory predicts that single-pulse probability drops below about 95% as the dimensionless energy $E^{*}$ passes roughly 20 and that multipulse states become entropically preferred past roughly 40; if single-pulse output remains the rule well beyond those thresholds, the thermodynamic instability is not the limiting mechanism. As a spectral check, the DSR spectrum must show a Lorentzian central spike of width $\\Xi$ shrinking toward zero while the cutoff $\\Delta$ saturates; a spectrum that keeps broadening without a narrowing spike contradicts the probability-distribution assumption underlying the negative temperature.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the adiabatic solution of the Ginzburg-Landau equation that yields the truncated Lorentzian spectral profile in Eq. (2)."},{"cited_title":"Rudenkov, V","cited_arxiv_id":null,"evidence_quote":"Establishes the master diagram, the fidelity curve, and the dissipative-soliton-resonance parametric space used throughout."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the experimental Cr2+:ZnS chirped-pulse oscillator spectra and energy-scaling data that the theory is compared with."},{"cited_title":"Vanin, A","cited_arxiv_id":null,"evidence_quote":"Defines dissipative soliton resonance as the infinite-energy asymptotic that the paper's energy-scaling analysis extends."},{"cited_title":"Grelu, W","cited_arxiv_id":null,"evidence_quote":"Gives the kinetic-theory description of incoherent solitons that justifies treating the chirped pulse as a statistical ensemble of quasi-particles."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the thermodynamic theory of mode-locking self-start, including the noise-temperature interpretation used for the continuous-wave energy variable."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the quantum-noise numerical simulations used for the multipulsing probability statistics in Fig. 5."},{"cited_title":"Nazarenko, Wave turbulence , Vol","cited_arxiv_id":null,"evidence_quote":"Defines the optical-soliton thermodynamic quantities (entropy and internal energy) on which Eqs. (8)-(10) are based."}],"review_version":1}