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arxiv: 2602.13922 · v2 · submitted 2026-02-14 · 🪐 quant-ph · hep-ph

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Decoherence, Perturbations and Symmetry in Lindblad Dynamics -- Implications for Diffractive Dissociation

A.Y.Klimenko
Authors on Pith no claims yet

Pith reviewed 2026-05-15 21:59 UTC · model grok-4.3

classification 🪐 quant-ph hep-ph
keywords diffractive dissociationLindblad dynamicsdecoherence factorsymmetry constraintsproton collisionscross sectionsCPT invariance
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The pith

A decoherence factor of 0.89 describes single-diffraction cross sections in proton collisions with 4 percent RMS fit error.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper extends a perturbative Dyson-type treatment together with discrete-symmetry constraints from the Schrödinger and von Neumann equations to a dephasing Lindblad framework. Scaling relations derived from an odd-symmetric formulation with dual temporal conditions are then applied to published single- and double-diffractive data from ISR, UA4, UA5, CDF, D0, ALICE and E710 experiments. Single-diffraction cross sections are shown to fit a three-parameter model that includes the decoherence factor, reaching a relative RMS deviation of about 4 percent and improving on conventional approximations that omit decoherence. The extracted factor remains consistent at approximately 0.89 across single diffraction, double diffraction and direct E710 estimates, and is interpreted as evidence favoring CPT-invariant over CP-invariant dephasing.

Core claim

Extending discrete-symmetry constraints to the dephasing Lindblad framework produces scaling relations under which single-diffraction cross sections are described by a three-parameter fit with relative RMS deviation of approximately 4 percent; the fit yields a decoherence factor phi approximately equal to 0.89 that is consistent across single-diffraction, double-diffraction and E710-based estimates and is naturally read as phi equals 1 for CP-invariant dephasing but phi less than 1 for CPT-invariant dephasing, thereby favoring the latter.

What carries the argument

The odd-symmetric formulation involving dual temporal conditions, extended from closed-system equations to the Lindblad master equation, which supplies the scaling relations used to fit the diffractive cross sections.

If this is right

  • The same three-parameter description with phi approximately 0.89 also accounts for double-diffraction data.
  • Conventional models that neglect decoherence produce substantially larger deviations from the measured cross sections.
  • The framework distinguishes CP-invariant from CPT-invariant dephasing on the basis of the extracted phi value.
  • Consistency of phi across independent data sets (SD, DD and E710) supports the applicability of the Lindblad scaling relations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same symmetry-constrained Lindblad treatment could be tested against other open-system scattering processes at colliders.
  • Higher-precision data from future runs at the LHC or a future collider could tighten the numerical value of phi.
  • If the CPT-favoring interpretation holds, analogous decoherence signatures may appear in other high-energy processes governed by discrete symmetries.

Load-bearing premise

The perturbative Dyson-type treatment and discrete-symmetry constraints from closed-system equations extend directly to the open Lindblad framework without introducing uncontrolled higher-order terms or altering data selection.

What would settle it

New single-diffraction cross-section measurements at higher energies that deviate markedly from the scaling predicted by a decoherence factor of 0.89 would falsify the central claim.

Figures

Figures reproduced from arXiv: 2602.13922 by A.Y.Klimenko.

Figure 1
Figure 1. Figure 1: Interaction diagrams for proton (antiproton) single diffraction (SD, left) and double diffraction (DD, right) via Pomeron P exchange, often sketched as two-gluon colour-singlet. The central inset sketches the QCD-motivated ladder picture of the Pomeron, and its split at the triple-P vertex. σSD ∝ g 2 Pp1 gPp2 g3P(p2) F [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: SD cross-section 2σSD vs p (s). Experimental data are from ISR, UA4, UA5, CDF, E710, D0 and ALICE collaborations. Approximations: – – – SDF1 (colour) or SDC1 (black), · · · · · · SDF2 (colour) or SDC4 (black), · – · – · – SDCln. The ISR experiments were conducted at lower energies and this makes SD measurements easier despite using older equipment—one can see that the error bars reported in [PITH_FULL_IMA… view at source ↗
Figure 3
Figure 3. Figure 3: DD cross-section σDD vs p (s). Experimental data are from UA5, CDF and ALICE collaborations. Approximations: – – – DDF1 (colour) or DDC1 (black), · · · · · · DDF2 7. Discussion This work yields a theoretical prediction by extending perturbative and discrete symmetry analysis from the von Neumann to the Lindblad framework. These results allow us to improve the approximation of single-diffraction (SD) cross-… view at source ↗
read the original abstract

We extend a perturbative Dyson-type treatment and discrete-symmetry constraints from the Schr\"{o}dinger and von Neumann equations to a dephasing Lindblad framework. This work develops further the odd-symmetric formulation involving dual temporal conditions from general dynamical considerations to specific tools of quantum mechanics. Applying the resulting scaling relations to published single- and double-diffractive data in $pp$ and $p\bar{p}$ collisions (ISR, UA4, UA5, CDF, D0, ALICE, and E710), we show that single-diffraction cross sections are well described by a three-parameter fit with a relative RMS deviation of $\sim 4\%$, substantially improving upon conventional approximations that neglect decoherence. The extracted decoherence factor is consistently $\phi \approx 0.89$, in agreement across SD, DD, and E710-based (direct) estimates, and is naturally interpreted as $\phi =1$ for CP-invariant dephasing but $\phi <1$ for CPT-invariant dephasing, favouring the latter.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript extends a perturbative Dyson-type treatment and discrete-symmetry constraints (including odd-symmetric dual-temporal conditions) from the Schrödinger/von Neumann equations to a dephasing Lindblad master equation. It derives scaling relations for diffractive amplitudes and applies them to published single- and double-diffractive cross-section data from ISR, UA4, UA5, CDF, D0, ALICE, and E710 experiments, reporting that a three-parameter fit (including decoherence factor φ) describes single-diffraction cross sections with ~4% relative RMS deviation, substantially better than conventional approximations, with a consistent extracted value φ ≈ 0.89 interpreted as favoring CPT-invariant dephasing.

Significance. If the extension of closed-system symmetries and perturbation theory to the Lindblad framework is valid without uncontrolled corrections, the work supplies a physically motivated phenomenological model for diffractive dissociation that incorporates decoherence via a single consistent parameter, improving data description and offering a potential link between open-system dynamics and high-energy scattering observables.

major comments (3)
  1. [§3] §3 (Lindblad extension): The claim that the odd-symmetric dual-temporal conditions and perturbative scaling relations carry over unchanged from the von Neumann equation to the dephasing Lindblad generator requires explicit derivation; the manuscript does not verify that the dissipator terms commute with the symmetry operators or introduce no additional contributions at the same perturbative order used for the diffractive amplitude.
  2. [§5] §5 (data analysis): The three-parameter fit achieves ~4% RMS on single-diffraction data, but φ is extracted from the same datasets (SD, DD, E710) to which the model is then applied; without an independent theoretical constraint or cross-validation on held-out data, the reported consistency of φ ≈ 0.89 across processes is by construction and does not constitute a prediction.
  3. [§4] §4 (perturbative treatment): No error propagation, covariance matrix, or assessment of higher-order terms in the Dyson expansion is provided; this leaves open whether the extracted φ absorbs uncontrolled corrections from the open-system generator rather than isolating decoherence.
minor comments (2)
  1. Notation for the decoherence factor φ and its relation to CP/CPT invariance should be defined more explicitly in the main text rather than relying on the abstract.
  2. Figure captions for the cross-section plots could include the exact parameter values and RMS values for each dataset to improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful review and valuable comments on our manuscript. We address each of the major comments below and outline the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: [§3] §3 (Lindblad extension): The claim that the odd-symmetric dual-temporal conditions and perturbative scaling relations carry over unchanged from the von Neumann equation to the dephasing Lindblad generator requires explicit derivation; the manuscript does not verify that the dissipator terms commute with the symmetry operators or introduce no additional contributions at the same perturbative order used for the diffractive amplitude.

    Authors: We agree that an explicit verification is necessary to fully substantiate the extension. In the revised manuscript, we will add a dedicated subsection in §3 deriving the action of the dephasing Lindblad dissipator under the odd-symmetric dual-temporal conditions. Specifically, we will show that for the form of the dissipator employed (which is diagonal in the chosen basis), it commutes with the relevant symmetry operators, ensuring no additional perturbative contributions at the order considered. This will confirm that the scaling relations remain unchanged. revision: yes

  2. Referee: [§5] §5 (data analysis): The three-parameter fit achieves ~4% RMS on single-diffraction data, but φ is extracted from the same datasets (SD, DD, E710) to which the model is then applied; without an independent theoretical constraint or cross-validation on held-out data, the reported consistency of φ ≈ 0.89 across processes is by construction and does not constitute a prediction.

    Authors: We acknowledge the referee's point regarding the potential circularity in the consistency claim. While the primary fit is performed on the single-diffractive (SD) datasets from multiple experiments, the values for double-diffractive (DD) and E710 are used to cross-check the extracted φ. To address this, we will revise §5 to clearly separate the fitting procedure (using SD data only for parameter determination) from the validation on DD and E710 data, and include a note on the limitations of not having fully held-out data. We maintain that the theoretical motivation for the model and the consistency across independent experiments provide supporting evidence beyond mere fitting. revision: partial

  3. Referee: [§4] §4 (perturbative treatment): No error propagation, covariance matrix, or assessment of higher-order terms in the Dyson expansion is provided; this leaves open whether the extracted φ absorbs uncontrolled corrections from the open-system generator rather than isolating decoherence.

    Authors: We agree that a more rigorous error analysis would improve the manuscript. In the revision, we will include the covariance matrix from the three-parameter fit, propagate uncertainties to the extracted φ, and provide an assessment of higher-order terms in the Dyson expansion by estimating their magnitude through comparison with available higher-energy data or bounding arguments. This will help clarify that φ primarily captures the decoherence effect rather than higher-order corrections. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected; derivation remains self-contained.

full rationale

The paper derives scaling relations by extending Dyson perturbation and discrete symmetries from the von Neumann equation to a dephasing Lindblad master equation, then applies those relations to fit three parameters (including the decoherence factor ϕ) to published diffraction datasets. This is explicitly framed as a fit that describes the data with ~4% RMS deviation, with ϕ extracted and checked for consistency across SD, DD, and E710 subsets. No quoted step reduces a claimed prediction or first-principles result to the fitted inputs by construction, nor does any load-bearing premise collapse to a self-citation or ansatz smuggled from prior work. The central claim is therefore a phenomenological improvement over decoherence-neglecting approximations rather than a closed tautology.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim depends on one fitted parameter and two domain assumptions about the applicability of Lindblad dynamics and symmetry constraints to high-energy collisions.

free parameters (1)
  • decoherence factor φ
    Fitted to single- and double-diffraction cross-section data; value ≈0.89 is extracted rather than derived from first principles.
axioms (2)
  • domain assumption Lindblad master equation form is valid for dephasing in diffractive processes
    Invoked when extending the perturbative treatment from Schrödinger/von Neumann to open-system dynamics.
  • domain assumption Discrete symmetry constraints carry over unchanged to the Lindblad framework
    Used to derive the odd-symmetric formulation and scaling relations.

pith-pipeline@v0.9.0 · 5480 in / 1449 out tokens · 18012 ms · 2026-05-15T21:59:12.517209+00:00 · methodology

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Reference graph

Works this paper leans on

61 extracted references · 61 canonical work pages · 12 internal anchors

  1. [1]

    The arrow of time.American Journal of Physics, 30(6):403–410, 1962/

    Thomas Gold. The arrow of time.American Journal of Physics, 30(6):403–410, 1962/. doi:10.1119/1.1942052

    work page doi:10.1119/1.1942052 1962

  2. [2]

    Oxford University Press, 1996

    Huw Price.Time’s Arrow and Archimedes’ Point: New Directions for the Physics of Time. Oxford University Press, 1996

    work page 1996

  3. [3]

    Schulman

    Lawrence S. Schulman. Models for intermediate time dynamics with two-time boundary conditions.Physica A: Statistical Mechanics and its Applications, 177(3):373–382, 1991. doi:10.1016/0378-4371(91)90175-C

    work page doi:10.1016/0378-4371(91)90175-c 1991

  4. [4]

    Schulman.Time’s Arrows and Quantum Measurement

    Lawrence S. Schulman.Time’s Arrows and Quantum Measurement. Cambridge University Press, 1997

    work page 1997

  5. [5]

    Boltzmann bridges

    Jordan Scharnhorst, David Wolpert, and Carlo Rovelli. Boltzmann bridges. 2024.doi: 10.48550/arXiv.2407.02840,arXiv:2407.02840

    work page doi:10.48550/arxiv.2407.02840 2024

  6. [6]

    A. Y. Klimenko. Two types of temporal symmetry in the laws of nature.Entropy, 27(5):466, 2025.doi:10.3390/e27050466,arXiv:2506.15730

    work page doi:10.3390/e27050466 2025

  7. [7]

    Percival

    Nicolas Gisin and Ian C. Percival. The quantum-state diffusion model applied to open systems.Journal of Physics A: Mathematical and General, 25(21):5677–5691, 1992.doi: 10.1088/0305-4470/25/21/023

    work page doi:10.1088/0305-4470/25/21/023 1992

  8. [8]

    Wiseman and Gerard J

    Howard M. Wiseman and Gerard J. Milburn.Quantum Measurement and Control. Cam- bridge University Press, 2010.doi:10.1017/CBO9780511813948

    work page doi:10.1017/cbo9780511813948 2010

  9. [9]

    Canonical hamiltonian ensemble representation of dephasing dynamics and the impact of thermal fluctuations on quantum-to-classical 23 transition.Scientific Reports, 11(1), 2021

    Hong-Bin Chen and Yueh-Nan Chen. Canonical hamiltonian ensemble representation of dephasing dynamics and the impact of thermal fluctuations on quantum-to-classical 23 transition.Scientific Reports, 11(1), 2021. Published 11 May 2021.doi:10.1038/s415 98-021-89400-3

    work page doi:10.1038/s415 2021

  10. [10]

    Giusteri

    Pietro De Checchi, Federico Gallina, Barbara Fresch, and Giulio G. Giusteri. On the noisy road to open quantum dynamics: The place of stochastic hamiltonians.Annalen der Physik, 538(1), 2026. Early View: 29 Dec 2025; arXiv:2510.10137.doi:10.1002/an dp.202500482,arXiv:2510.10137

    work page doi:10.1002/an 2026

  11. [11]

    Bergmann, and Joel L

    Yakir Aharonov, Peter G. Bergmann, and Joel L. Lebowitz. Time symmetry in the quantum process of measurement.Physical Review, 134(6B):B1410–B1416, 1964.doi: 10.1103/PhysRev.134.B1410

    work page doi:10.1103/physrev.134.b1410 1964

  12. [12]

    The Two-State Vector Formalism

    Lev Vaidman. The two-state vector formalism. 2007.doi:10.48550/arXiv.0706.1347, arXiv:0706.1347

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.0706.1347 2007

  13. [13]

    Georgiou

    Olga Movilla Miangolarra, Ralph Sabbagh, and Tryphon T. Georgiou. Quantum schrodinger bridges: large deviations and time-symmetric ensembles. 2025.doi: 10.48550/arXiv.2503.05886,arXiv:2503.05886

    work page doi:10.48550/arxiv.2503.05886 2025

  14. [14]

    A. Y. Klimenko. Symmetric and antisymmetric forms of the Pauli master equation. Scientific Reports, 6:29942, 2016.doi:10.1038/srep29942,arXiv:1611.04582

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1038/srep29942 2016

  15. [15]

    C. Ou, R. V. Chamberlin, and S. Abe. Lindbladian operators, von Neumann entropy and energy conservation in time-dependent quantum open systems.Physica A: Statistical Mechanics and its Applications, 466:450–454, 2017

    work page 2017

  16. [16]

    M. Tamm. Is causality a necessary tool for understanding our universe, or is it a part of the problem?Entropy, 23(7):886, 2021.doi:10.3390/e23070886

    work page doi:10.3390/e23070886 2021

  17. [17]

    Schirmer and Allan I

    Sonia G. Schirmer and Allan I. Solomon. Constraints on relaxation rates for n-level quantum systems.Physical Review A, 70(2):022107, 2004.doi:10.1103/PhysRevA.70. 022107

    work page doi:10.1103/physreva.70 2004

  18. [18]

    Daniel K. L. Oi and Sophie G. Schirmer. Limits on the decay rate of quantum coherence and correlation.Physical Review A, 86(1):012121, 2012.doi:10.1103/PhysRevA.86.01 2121,arXiv:1109.0954

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physreva.86.01 2012

  19. [19]

    A. Y. Klimenko. On the effect of decoherence on quantum tunnelling.SN Applied Sciences, 3(7):710, 2021.doi:10.1007/s42452-021-04675-5,arXiv:2011.12955

    work page doi:10.1007/s42452-021-04675-5 2021

  20. [20]

    Pure dephasing of light-matter systems in the ultrastrong and deep-strong coupling regimes.Physical Review Letters, 130(12), 2023.doi:10.1103/physrevlett.130.123601

    Alberto Mercurio, Shilan Abo, Fabio Mauceri, Enrico Russo, Vincenzo Macr` ı, Adam Miranowicz, Salvatore Savasta, and Omar Di Stefano. Pure dephasing of light-matter systems in the ultrastrong and deep-strong coupling regimes.Physical Review Letters, 130(12), 2023.doi:10.1103/physrevlett.130.123601. URL:https://doi.org/10.1 103/PhysRevLett.130.123601

    work page doi:10.1103/physrevlett.130.123601 2023

  21. [21]

    A short introduction to the Lindblad master equation.AIP Advances, 10(2):025106, 2020.doi:10.1063/1.5115323,arXiv:1906.04478

    Daniel Manzano. A short introduction to the Lindblad master equation.AIP Advances, 10(2):025106, 2020.doi:10.1063/1.5115323,arXiv:1906.04478

    work page doi:10.1063/1.5115323 2020

  22. [22]

    Gough, Hendra I

    Franco Fagnola, John E. Gough, Hendra I. Nurdin, and Lorenza Viola. Mathematical models of markovian dephasing.Journal of Physics A: Mathematical and Theoretical, 52(38):385301, 2019.doi:10.1088/1751-8121/ab38ec,arXiv:1811.11784

    work page doi:10.1088/1751-8121/ab38ec 2019

  23. [23]

    Daniel Puzzuoli, Sophia Fuhui Lin, Moein Malekakhlagh, Emily Pritchett, Benjamin Rosand, and Christopher J. Wood. Algorithms for perturbative analysis and simu- lation of quantum dynamics.Journal of Computational Physics, 489:112262, 2023. arXiv:2210.11595 [quant-ph].doi:10.1016/j.jcp.2023.112262,arXiv:2210.11595

    work page doi:10.1016/j.jcp.2023.112262 2023

  24. [24]

    Moein Malekakhlagh, Alireza Seif, Daniel Puzzuoli, Luke C. G. Govia, and Ewout van den Berg. Efficient Lindblad synthesis for noise model construction.npj Quantum Informa- tion, 11(1):191, 2025. arXiv:2502.03462 [quant-ph].doi:10.1038/s41534-025-01139-1, arXiv:2502.03462

    work page doi:10.1038/s41534-025-01139-1 2025

  25. [25]

    J. McL. Emmerson.Symmetry principles in particle physics. Clarendon Press, Oxford, 1972

    work page 1972

  26. [26]

    A. Y. Klimenko. Note on invariant properties of a quantum system placed into thermo- dynamic environment.Physica A: Statistical Mechanics and its Applications, 398:65–75, 2014.doi:10.1016/j.physa.2013.11.037,arXiv:1402.3864

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physa.2013.11.037 2014

  27. [27]

    A. Y. Klimenko. Kinetics of interactions of matter, antimatter and radiation consistent with antisymmetric (cpt-invariant) thermodynamics.Entropy, 19(5):202, 2017.doi: 24 10.3390/e19050202

    work page doi:10.3390/e19050202 2017

  28. [28]

    M. L. Good and W. D. Walker. Diffraction dissociation of beam particles.Physical Review, 120:1857–1860, 1960.doi:10.1103/PhysRev.120.1857

    work page doi:10.1103/physrev.120.1857 1960

  29. [29]

    V. A. Khoze, M. G. Ryskin, and M. Taˇ sevsk´ y. High energy soft QCD and diffraction. Review inReview of Particle Physics(Particle Data Group), 2023. Appears as a PDG review (RPP 2022 edition); revised Aug 2023. Journal anchor: [57]. URL:https://pdg. lbl.gov/2023/reviews/rpp2022-rev-soft-qcd.pdf

    work page 2023

  30. [30]

    Theoretical and Mathematical Physics

    Vincenzo Barone and Enrico Predazzi.High-Energy Particle Diffraction. Theoretical and Mathematical Physics. Springer, Berlin, Heidelberg, 2002. Print ISBN 3-540-42107-6; eBook DOI/ISBN corresponds to the Springer electronic edition.doi:10.1007/978-3-6 62-04724-8

    work page doi:10.1007/978-3-6 2002

  31. [31]

    Review of particle physics

    S. Navas et al. Review of particle physics.Physical Review D, 110:030001, 2024.doi: 10.1103/PhysRevD.110.030001

    work page doi:10.1103/physrevd.110.030001 2024

  32. [32]

    E. A. De Wolf. Diffractive scattering.Journal of Physics G: Nuclear and Particle Physics, 28(5):1023–1044, 2002.doi:10.1088/0954-3899/28/5/324,arXiv:hep-ph/0203074

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0954-3899/28/5/324 2002

  33. [33]

    I. Ya. Pomeranchuk. On the asymptotic equality of particle and antiparticle cross sections. Soviet Physics JETP, 7:499–501, 1958. English translation of Zh. Eksp. Teor. Fiz. 34 (1958) 725. URL:https://jetp.ras.ru/cgi-bin/dn/e_007_03_0499.pdf

    work page 1958

  34. [34]

    Total cross sections

    A. Donnachie and P. V. Landshoff. Total cross sections.Physics Letters B, 296:227–232, 1992.doi:10.1016/0370-2693(92)90832-O,arXiv:hep-ph/9209205

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/0370-2693(92)90832-o 1992

  35. [35]

    P. D. B. Collins.An Introduction to Regge Theory and High Energy Physics. Cambridge University Press, Cambridge, 1977.doi:10.1017/CBO9780511897603

    work page doi:10.1017/cbo9780511897603 1977

  36. [36]

    roman pot

    R. Battiston et al. The “roman pot” spectrometer and the vertex detector of experiment UA4 at the CERN SPS collider.Nuclear Instruments and Methods in Physics Research Section A, 238:35–44, 1985.doi:10.1016/0168-9002(85)91024-1

    work page doi:10.1016/0168-9002(85)91024-1 1985

  37. [37]

    M. G. Albrow et al. Inelastic diffraction at the CERN ISR.Nuclear Physics B, 108:1–29,

    work page

  38. [38]

    Often cited as the CHLM ISR diffraction measurement.doi:10.1016/0550-321 3(76)90121-8

    work page doi:10.1016/0550-321

  39. [39]

    J. C. M. Armitage et al. Single diffraction dissociation in proton–proton collisions at ISR energies.Nuclear Physics B, 194:365–396, 1982.doi:10.1016/0550-3213(82)90014-1

    work page doi:10.1016/0550-3213(82)90014-1 1982

  40. [40]

    R. E. Ansorge et al. Diffraction dissociation at the CERN proton–antiproton collider at centre-of-mass energies of 900 and 200 GeV.Z. Phys. C, 33:175–185, 1986.doi: 10.1007/BF01411134

    work page doi:10.1007/bf01411134 1986

  41. [41]

    Abramowicz

    H. Abramowicz. Diffraction and the pomeron.International Journal of Modern Physics A, 15(Suppl. 1B):495–520, 2000.doi:10.1142/S0217751X00005292,arXiv:hep-ph/00 01054

    work page doi:10.1142/s0217751x00005292 2000

  42. [42]

    M. G. Poghosyan. Two remarks about UA5 published data on inelastic and diffractive cross sections. 2010.arXiv:1005.1806

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  43. [43]

    Bernard et al

    D. Bernard et al. The cross section of single diffraction dissociation form 2 x/s≤0.05 at√s= 546 GeV.Physics Letters B, 186:227–232, 1987.doi:10.1016/0370-2693(87)902 85-1

    work page doi:10.1016/0370-2693(87)902 1987

  44. [44]

    Abe et al

    F. Abe et al. Measurement of ¯ppsingle diffraction dissociation at √s= 546 and 1800 GeV.Phys. Rev. D, 50:5535–5549, 1994.doi:10.1103/PhysRevD.50.5535

    work page doi:10.1103/physrevd.50.5535 1994

  45. [45]

    Arnab Kumar Pal.Measurement Of Single Diffractive Differential Cross Section (dσ/d|t|) At √s= 1.96TeV Using The DØ Forward Proton Detectors. Ph.d. thesis, The University of Texas at Arlington, Arlington, TX, USA, August 2011. Dissertation. Also issued as FERMILAB-THESIS-2011-56; PDF:https://lss.fnal.gov/archive/thesis/2000/f ermilab-thesis-2011-56.pdf

    work page 2011

  46. [46]

    Transverse momentum spectra of charged particles in proton-proton collisions at $\sqrt{s} = 900$ GeV with ALICE at the LHC

    K. Aamodt et al. Transverse momentum spectra of charged particles in proton–proton collisions at √s= 900 gev with ALICE at the LHC.Physics Letters B, 693:53–68, 2010. doi:10.1016/j.physletb.2010.08.026,arXiv:1007.0719

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2010.08.026 2010

  47. [47]

    Measurement of inelastic, single- and double-diffraction cross sections in proton-proton collisions at the LHC with ALICE

    B. Abelev et al. Measurement of inelastic, single- and double-diffraction cross sections in proton–proton collisions at the LHC with ALICE.Eur. Phys. J. C, 73:2456, 2013. doi:10.1140/epjc/s10052-013-2456-0,arXiv:1208.4968. 25

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-013-2456-0 2013

  48. [48]

    M. G. Poghosyan. Diffraction dissociation in proton-proton collisions at the LHC with ALICE.Journal of Physics G: Nuclear and Particle Physics, 38:124044, 2011.doi: 10.1088/0954-3899/38/12/124044,arXiv:1109.4510

    work page doi:10.1088/0954-3899/38/12/124044 2011

  49. [49]

    N. A. Amos et al. A luminosity-independent measurement of the ¯pptotal cross section at √s= 1.8 TeV.Physics Letters B, 243:158–164, 1990. Contains a determination of the total single-diffractive cross section and side-separated single-arm yields.doi: 10.1016/0370-2693(90)90973-A

    work page doi:10.1016/0370-2693(90)90973-a 1990

  50. [50]

    N. A. Amos et al. Diffraction dissociation in ¯ppcollisions at √s= 1.8 TeV.Physics Letters B, 301:313–316, 1993.doi:10.1016/0370-2693(93)90707-0

    work page doi:10.1016/0370-2693(93)90707-0 1993

  51. [51]

    POMERON FLUX RENORMALIZATION IN SOFT AND HARD DIFFRACTION

    K. Goulianos. Renormalization of hadronic diffraction and the structure of the pomeron. Physics Letters B, 358(3–4):379–388, 1995.doi:10.1016/0370- 2693(95)01023-J, arXiv:hep-ph/9502356

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/0370- 1995

  52. [52]

    Affolder et al

    T. Affolder et al. Double diffraction dissociation at the fermilab tevatron collider.Phys. Rev. Lett., 87:141802, 2001.doi:10.1103/PhysRevLett.87.141802,arXiv:hep-ex/01 07070

    work page doi:10.1103/physrevlett.87.141802 2001

  53. [53]

    V. M. Abazov et al. Odderon exchange from elastic scattering differences betweenpp and ¯ppdata at 1.96 TeV and fromppforward scattering measurements.Physical Review Letters, 127:062003, 2021.doi:10.1103/PhysRevLett.127.062003,arXiv:2012.03981

    work page doi:10.1103/physrevlett.127.062003 2021

  54. [54]

    Pich and M

    A. Pich and M. Ramsey-Musolf. Tests of conservation laws. Review inReview of Particle Physics(Particle Data Group), 2020. Written Aug 2019; PDG review (RPP 2020 edition). Journal anchor: [58]. URL:https://pdg.lbl.gov/2021/reviews/rpp2020-rev-conse rvation-laws.pdf

    work page 2020

  55. [55]

    A. Y. Klimenko and U. Maas. One antimatter—two possible thermodynamics.Entropy, 16(3):1191–1210, 2014.doi:10.3390/e16031191,arXiv:1404.0205

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3390/e16031191 2014

  56. [56]

    A. Y. Klimenko. Mixing, tunnelling and the direction of time in the context of Re- ichenbach’s principles. In Jan de Gier, Cheryl E. Praeger, and Terence Tao, editors, 2019-20 MATRIX Annals, pages 387–409. Springer International Publishing, Cham, 2021. doi:10.1007/978-3-030-62497-2_23,arXiv:2001.00527

    work page doi:10.1007/978-3-030-62497-2_23 2019

  57. [57]

    A. Y. Klimenko. On thermodynamics and kinetics of antisystems.Combustion Theory and Modelling, pages 1–36, 2026.doi:10.1080/13647830.2026.2613889

    work page doi:10.1080/13647830.2026.2613889 2026

  58. [58]

    R. L. Workman et al. Review of particle physics.Progress of Theoretical and Experimental Physics, 2022(8):083C01, 2022.doi:10.1093/ptep/ptac097

    work page doi:10.1093/ptep/ptac097 2022

  59. [59]

    P. A. Zyla et al. Review of particle physics.Progress of Theoretical and Experimental Physics, 2020(8):083C01, 2020.doi:10.1093/ptep/ptaa104

    work page doi:10.1093/ptep/ptaa104 2020

  60. [60]

    On the generators of quantum dynamical semigroups.Communications in Mathematical Physics, 48(2):119–130, 1976.doi:10.1007/BF01608499

    G¨ oran Lindblad. On the generators of quantum dynamical semigroups.Communications in Mathematical Physics, 48(2):119–130, 1976.doi:10.1007/BF01608499

    work page doi:10.1007/bf01608499 1976

  61. [61]

    Symmetries and conserved quantities in Lindblad master equations

    Victor V. Albert and Liang Jiang. Symmetries and conserved quantities in Lindblad master equations.Physical Review A, 89(2):022118, 2014.doi:10.1103/PhysRevA.89. 022118,arXiv:1310.1523. Appendix A. The dephasing Lindblad equation preserving energy Consider the pure-dephasing Lindblad equation [59] dρ dt =L(ρ) (A1) =− i ℏ[H, ρ]− 1 ℏ2 X j γj LjρL† j − 1 2 n...

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physreva.89 2014