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arxiv: 2606.10886 · v1 · pith:RZXLMQAAnew · submitted 2026-06-09 · ⚛️ physics.gen-ph

Belief in thermodynamics has provoked false thermodynamics of superconductors

A.V. Nikulov This is my paper

Pith reviewed 2026-06-27 10:27 UTC · model grok-4.3

classification ⚛️ physics.gen-ph
keywords superconductivitythermodynamicsMeissner effectsecond lawGorter cyclefree energyphase transition
0
0 comments X

The pith

The Meissner effect violates the second law of thermodynamics due to negative surplus work in the Gorter cycle.

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

The paper argues that belief in the equality of free energies at the superconducting transition in the critical magnetic field cannot be maintained without contradicting the second law of thermodynamics. This has led to a false thermodynamics of superconductors that also violates the law of conservation of energy. The Meissner effect is identified as performing negative surplus work in the closed Gorter cycle. A sympathetic reader would care because it indicates that the conventional theory of superconductivity is inconsistent with basic thermodynamic principles.

Core claim

The common belief that the superconducting transition occurs when the free energy of the superconducting state becomes less than of the normal state has provoked a false claim that a power source of a solenoid creates the energy of magnetization rather than of magnetic field. No one has noticed that the equality of free energies at the superconducting transition in the critical magnetic field cannot be obtained without contradicting the second law of thermodynamics. The Meissner effect violates the second law of thermodynamics because of the negative surplus work performed in the closed Gorter cycle. The desire to avoid contradiction of superconductivity phenomena with the second law of ther

What carries the argument

The Gorter cycle, which reveals the negative surplus work performed during the superconducting transition.

If this is right

  • The power source of a solenoid creates the energy of the magnetic field rather than the energy of magnetization.
  • The standard thermodynamic description of the superconducting transition must be abandoned to resolve the contradiction with the second law.
  • The Meissner effect requires a new explanation that does not violate thermodynamic laws.

Where Pith is reading between the lines

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

  • If the analysis holds, the energy accounting for magnetic fields in superconducting devices would need re-examination.
  • This raises the possibility that equilibrium assumptions in other quantum condensed matter systems may also require thermodynamic re-assessment.

Load-bearing premise

The classical thermodynamic analysis of work and heat in the Gorter cycle applies directly to the superconducting transition without additional quantum corrections.

What would settle it

A direct measurement of the work performed in a closed Gorter cycle on a superconductor showing non-negative surplus work would falsify the claim.

read the original abstract

Belief in thermodynamics has forced superconductivity experts to forget basics of thermodynamics due to a contradiction of superconductivity phenomena to laws of thermodynamics. Because of this belief no one drew reader's attention during many years that the conventional theory of superconductivity contradicts to the second law of thermodynamics. The common belief that the superconducting transition occurs when the free energy of the superconducting state becomes less than of the normal state has provoked a false claim that a power source of a solenoid creates the energy of magnetization rather than of magnetic field. The authors of only a few books on superconductivity, mostly future Nobel prize winners, did not follow this false claim. No one for many years has noticed that the equality of free energies at the superconducting transition in the critical magnetic field cannot be obtained without contradicting the second law of thermodynamics. The Meissner effect violates the second law of thermodynamics because of the negative surplus work performed in the closed Gorter cycle. The desire to avoid contradiction of superconductivity phenomena with the second law of thermodynamics provoked the false thermodynamics of superconductors, contradicting the law of conservation of energy.

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

2 major / 1 minor

Summary. The manuscript argues that the conventional thermodynamic treatment of the superconducting transition—including the equality of free energies at the critical field Hc and the analysis of the closed Gorter cycle—contradicts the second law of thermodynamics due to negative surplus work from the Meissner effect. It claims this has led to false thermodynamics of superconductors that also violates energy conservation, and that the free-energy equality cannot be obtained consistently.

Significance. If the central claim were substantiated by explicit derivations, the result would be highly significant as a fundamental challenge to the thermodynamic foundations of superconductivity, requiring re-examination of magnetic work terms and phase-transition analysis in type-I materials. No such substantiation is provided.

major comments (2)
  1. [Abstract] Abstract: The assertion that the closed Gorter cycle produces negative surplus work (violating the second law) is made without any explicit path-integral evaluation of net work ∮δW, without reference to the Gibbs relation dG = −S dT − μ0 M dH, and without accounting for the latent heat or entropy discontinuity at the first-order transition. This calculation is load-bearing for the central claim.
  2. [Abstract] Abstract: The claim that free-energy equality at the transition in Hc cannot be obtained without contradicting the second law treats the conventional equality both as premise and as the source of inconsistency, without supplying an independent derivation of the magnetic work term outside the standard framework; the argument therefore risks circularity.
minor comments (1)
  1. The manuscript consists almost entirely of assertions; addition of at least one fully worked cycle diagram with explicit signs for each leg (isothermal field ramp above Tc, isofield cooling, etc.) would be required for the claims to be evaluable.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below and indicate where revisions will be made to strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that the closed Gorter cycle produces negative surplus work (violating the second law) is made without any explicit path-integral evaluation of net work ∮δW, without reference to the Gibbs relation dG = −S dT − μ0 M dH, and without accounting for the latent heat or entropy discontinuity at the first-order transition. This calculation is load-bearing for the central claim.

    Authors: The manuscript presents a conceptual demonstration that the Meissner expulsion in the closed Gorter cycle yields net negative work when the cycle returns to the initial state. We agree that an explicit evaluation would improve rigor. In revision we will add a dedicated section computing ∮δW via the Gibbs relation, explicitly including the latent-heat and entropy-discontinuity contributions at the first-order transition to quantify the surplus work. revision: yes

  2. Referee: [Abstract] Abstract: The claim that free-energy equality at the transition in Hc cannot be obtained without contradicting the second law treats the conventional equality both as premise and as the source of inconsistency, without supplying an independent derivation of the magnetic work term outside the standard framework; the argument therefore risks circularity.

    Authors: The reasoning is not circular. We start from the experimentally established Meissner effect together with the standard thermodynamic identity for magnetic work and then examine the consequences for a closed cycle. The resulting negative net work demonstrates that the conventional free-energy equality at Hc is thermodynamically inconsistent with the second law; the work term itself is derived from the field-expulsion process and does not presuppose the equality. revision: no

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper critiques conventional superconductivity theory by asserting that the standard free-energy equality at the transition and the Meissner effect produce negative surplus work in the Gorter cycle, violating the second law. This is framed as an inconsistency in existing interpretations rather than a derivation chain that reduces to its own inputs. The provided abstract contains no equations, no fitted parameters renamed as predictions, and no self-citations that serve as load-bearing premises. The central claim applies classical thermodynamic identities to known phenomena without self-definitional loops or ansatzes smuggled via prior work by the same authors.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that classical thermodynamic cycles and the second law apply unchanged to the superconducting state, plus the description of the Meissner effect and Gorter cycle taken from prior literature. No free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The second law of thermodynamics and the definition of thermodynamic work apply directly to the superconducting transition and the Meissner effect without quantum or non-equilibrium corrections.
    Invoked when the abstract equates free energies at the critical field and identifies negative surplus work in the Gorter cycle.

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Reference graph

Works this paper leans on

109 extracted references · 27 canonical work pages

  1. [1]

    Whether the the- ory of hole superconductivity can explain such observa- tions consistent with thermodynamics is an open ques- tion” [1]

    is another example of violation of the second law of thermodynamics by superconductors. Whether the the- ory of hole superconductivity can explain such observa- tions consistent with thermodynamics is an open ques- tion” [1]. This question cannot be consider as open. The Hirsch theory, in contrast to the conventional theory of [7, 34], cannot explain in p...

  2. [2]

    F ALSE CLAIM OF GOR TER AND CASIMIR. Almost no one pays attention to the experimental evi- dences [19–23, 57] of violations of the second law of ther- modynamics predicted [46, 53, 54] by the conventional theory of superconductivity [7, 34], since this law has al- ways been a matter of faith rather than understanding. Most scientists in the late 19th and ...

    1914

  3. [3]

    4-A Congr

    published in 1938: ”The idea of applying thermody- namics to the transition from the superconducting to the normal state was first expressed by Keesom (1924 Rapp. 4-A Congr. Phys. Solvay, 288) and then by Rutgers [62] and developed in detail by Gorter [63]”. The doubts about the reversibility of the supercon- ducting transition that existed before the dis...

    1938

  4. [4]

    Jorge Hirsch, unlike the authors of most books [16, 64– 68] and like V.L

    HIRSCH REPEA TED A MIST AKE MADE BY GOR TER AND CASIMIR. Jorge Hirsch, unlike the authors of most books [16, 64– 68] and like V.L. Ginzburg [69] and P.G. de Gennes [70] understands that the power source of the solenoid cre- ates the energy of magnetic fieldHB/2 rather than the energy−HM/2 of magnetizationM=B−µ 0H. He understands also that the same amount ...

    1934

  5. [5]

    switching off the magnetic fieldH= 0. In passing (in the beginning of process 3) the threshold value curve Hc(T), the electromotive force on the solenoid that main- tains the magnetic field must do an amount of work equal to twice the energy of the field that comes into existence in the metal” [17]. This cycle is called ’Gorter cycle’ by Hirsch in the art...

    1934

  6. [6]

    The total work in the Gorter cycle is posi- tive and equal the surplus workW G =W sn +W G4 = 2Em −E m =V µ 0H2 2 /2 =W surp according to the correct opinion

    the power source of the solenoid performs the posi- tive workW sn =V µ 0H2 2 = 2E m atH 2 =H c(T) and the negative workW G4 =−V µ 0H2 2 /2 =−E m during process 4. The total work in the Gorter cycle is posi- tive and equal the surplus workW G =W sn +W G4 = 2Em −E m =V µ 0H2 2 /2 =W surp according to the correct opinion. According to the false claim of C.J....

  7. [7]

    Gorter and H

    contradicts the second law of thermodynamics since he, like C.J. Gorter and H. Casimir [63], forgot that the law of conservation of energy must be valid not only for a closed cycle. Equation (10) in [1] should repeat equation (9) (equation (11) in [63]) since it is also deduced on the base of the law of conservation of energy in the Gorter cycle: the tota...

  8. [8]

    Many of the mistakes made in the article [1] would have been impossible if J

    ARBITRARINESS IN DEFINITIONS IS NOT ACCEPT ABLE IN SCIENCE. Many of the mistakes made in the article [1] would have been impossible if J. Hirsch had paid attention to the contradictions between books on superconductivity and read carefully the article of C.J. Gorter and H. Casimir [63]. The contradictions between books are the result of neglecting one of ...

    1946

  9. [9]

    describe the Gibbs free energy although neither Gibss free energy nor any other free energy can increase when no work is done on a body, contrary to (6), and must increase when work is done, contrary to (5). M. Tinkham [71], in contrast to the authors [16, 64– 67], did not follow to the false claim of C.J. Gorter and H. Casimir [63]. But he used also the ...

  10. [10]

    The three options of the free energy in the normal state demonstrate once again that arbitrariness in definitions must not be acceptable in science

    work performed atH=H c ”equal to twice the en- ergy of the field that comes into existence in the metal” [17]. The three options of the free energy in the normal state demonstrate once again that arbitrariness in definitions must not be acceptable in science. In this case, the issue is most obvious, since the work done to create a magnetic field in the vo...

  11. [11]

    and A.A. Abrikosov [72]dG nH /dT=dG n0/dT− µ0HcdHc/dT=−S n −µ 0HcdHc/dT=dG sH /dT= dGs0/dT=−S s since free energies of two phases are equal according to equation (7) atT=T 2 andH 2 = Hc(T2) and therefore the first derivative of free energy with respect to temperatureS=−dF/dTcan be fi- nite. But the first derivative must be infinite according to equation (...

  12. [12]

    in the main. But he did not realize that his equation (13) in [1] is ”the basic equation of the thermodynamics of superconductors developed by Gorter and Casimir” (12) rather than the change in free energy during the super- conducting transition atH 2 =H c(T2). Therefore he used the trick of M. Tinkham [71]: ”The reader may wonder how Eq. (13) is consiste...

  13. [13]

    The numerous mistakes made by J

    REGRESS IN THE UNDERST ANDING OF THERMODYNAMICS. The numerous mistakes made by J. Hirsch in the article

  14. [14]

    The regression began a century ago when W.H

    indicate a regression in the understanding of thermo- dynamics that was provoked by the belief in thermody- namics. The regression began a century ago when W.H. Keesom (1924 Rapp. 4-A Congr. Phys. Solvay, 288) derived equation (15) for the latent heat, see the article [73]. This unreasonable belief that the superconducting transition atH=H c(T) is a first...

    1924

  15. [15]

    had to contradicts to the law of conservation of en- ergy by the claim that the workW sn =µ 0H2 c should not change either free energy or heat ∆U= ∆F+ ∆ST= 0

  16. [16]

    Gorter and H

    C.J. Gorter and H. Casimir [63], and the authors of most books [16, 64–68] had to contradict the second law of thermodynamics by the claim that the work changes heatµ 0H2 c = ∆ST. Various misconceptions appeared as early as 1934. W.H. Keesom, in contrast to C.J. Gorter and H. Casimir [63], understood that the power source of the solenoid creates magnetic ...

    1934

  17. [17]

    Keesom knew about the workW sn =µ 0H2 c performed atH=H c(T)

    W.H. Keesom knew about the workW sn =µ 0H2 c performed atH=H c(T)

  18. [18]

    Keesom understood that the half of the work Wsn =µ 0H2 c creates the energy of the magnetic field Em =µ 0H2 c /2, which is part of free energy

    W.H. Keesom understood that the half of the work Wsn =µ 0H2 c creates the energy of the magnetic field Em =µ 0H2 c /2, which is part of free energy. Because of the change in the free energy FnH =F sH +E m =F sH + µ0H2 c 2 (16) the transition cannot be a phase transition

  19. [19]

    W.H. Keesom imagined before the discovery of the Meissner effect that the second half of the work, the sur- plus workW surp =W sn −E m =µ 0H2 c /2, generates Joule heat: ”Till now we imagined that the surplus work served to deliver the Joule-heat developed by the persistent cur- rents the metal getting resistance while passing to the non-supraconductive c...

  20. [20]

    W.H. Keesom should have known until 1933 that the transition cannot be reversible since the magnetic flux cannot be pushed out of a perfect conductor in ac- cordance with physical laws known in 1933, such as Fara- day’s law and the law of angular momentum conserva- tion. The Meissner effect could eliminate only the fourth reason, and only experimentally, ...

    1933

  21. [21]

    This contradiction was ignored for many years, until J

    to this contradiction expresses the attitude of almost all experts on superconductivity. This contradiction was ignored for many years, until J. Hirsch began to pay at- tention to it. J. Hirsch expressed surprise in 2010 about the ignoring of the obvious contradiction: ”Strangely, the question of what is the force propelling the mobile charge carriers and...

    2010

  22. [22]

    This article draws attention to unpleas- ant truth

    CONCLUSION Scientists must pursue the Truth, even if the truth is unpleasant. This article draws attention to unpleas- ant truth. The false thermodynamics of superconductors provoked by belief in thermodynamics shows that blind faith and even superstition can play an important and even decisive role in science. Einstein understood that thermodynamics is n...

    1914

  23. [23]

    Hirsch, Does the Meissner effect violate the second law of thermodynamics?, Physica C 629 (2025) 1354618, doi: https://doi.org/10.1016/j.physc.2024.1354618

    J.E. Hirsch, Does the Meissner effect violate the second law of thermodynamics?, Physica C 629 (2025) 1354618, doi: https://doi.org/10.1016/j.physc.2024.1354618

    work page doi:10.1016/j.physc.2024.1354618 2025

  24. [24]

    Lieb and J

    E.H. Lieb and J. Yngvason, The physics and mathemat- ics of the second law of thermodynamics. Physics Reports 310 (1999) 1-96

    1999

  25. [25]

    M. Smoluchowski, Gultigkeitsgrenzen des zweiten Haupt- satzes der Warmetheorie, in Vortrage uber kinetische Theorie der Materie und der Elektrizitat (Mathematische Vorlesungen an der Universitat Gottingen, VI). Leipzig und Berlin, B.G.Teubner, 1914, p.87

    1914

  26. [26]

    Carnot, Reflections on the Motive Power of Heat and on Machines Fitted to Develop that Power

    S. Carnot, Reflections on the Motive Power of Heat and on Machines Fitted to Develop that Power. New York: J. Wiley and Sons, 1897

  27. [27]

    Nikulov, The Law of Entropy Increase and the Meissner Effect, Entropy 24 (2022) 83

    A.V. Nikulov, The Law of Entropy Increase and the Meissner Effect, Entropy 24 (2022) 83. https://doi.org/10.3390/e24010083

    work page doi:10.3390/e24010083 2022

  28. [28]

    Capek and D

    V. Capek and D. Sheehan, Challenges to the Second Law of Thermodynamics. Theory and Experiment; Springer: Berlin/Heidelberg, Germany, 2005

    2005

  29. [29]

    Bardeen, L.N

    J. Bardeen, L.N. Cooper, J.R. Schrieffer, Theory of Su- perconductivity, Phys. Rev. 108 (1957) 1175

    1957

  30. [30]

    Hirsch, BCS theory of superconductivity: it is time to question its validity, Phys

    J.E. Hirsch, BCS theory of superconductivity: it is time to question its validity, Phys. Scripta 80 (2009) 035702

    2009

  31. [31]

    Hirsch, Superconductivity Begins With H, World Scientific, 2020

    J.E. Hirsch, Superconductivity Begins With H, World Scientific, 2020

    2020

  32. [32]

    See https://jorge.physics.ucsd.edu/hole.html for a list of references

  33. [33]

    Hirsch, Hole superconductivity, OSF preprints, 2024, https://osf.io/preprints/osf/kpxufand references therein

    J.E. Hirsch, Hole superconductivity, OSF preprints, 2024, https://osf.io/preprints/osf/kpxufand references therein

    2024

  34. [34]

    Hirsch, Joule heating in the normal-superconductor phase transition in a magnetic field, Physica C 576 (2020) 1353687

    J.E. Hirsch, Joule heating in the normal-superconductor phase transition in a magnetic field, Physica C 576 (2020) 1353687

    2020

  35. [35]

    Hirsch, Inconsistency of the conventional theory of superconductivity

    J.E. Hirsch, Inconsistency of the conventional theory of superconductivity. EPL130, 17006 (2020)

    2020

  36. [36]

    Hirsch, Thermodynamic inconsistency of the con- ventional theory of superconductivity, Int

    J.E. Hirsch, Thermodynamic inconsistency of the con- ventional theory of superconductivity, Int. J. Mod. Phys. B 34 (2020) 2050175

    2020

  37. [37]

    Meissner and R

    W. Meissner and R. Ochsenfeld, Ein neuer Effekt bei Eintritt der Supraleitfahigkeit, Naturwiss. 21 (1933) 787-

    1933

  38. [38]

    https://doi.org/10.1007/BF01504252

    work page doi:10.1007/bf01504252

  39. [39]

    Shoenberg, Superconductivity, Cambridge, 1938

    D. Shoenberg, Superconductivity, Cambridge, 1938

    1938

  40. [40]

    Keesom and J.A

    W.H. Keesom and J.A. Kok, Further calorimetric experiments on thallium, Physica 1 (1934) 595-608. https://doi.org/10.1016/S0031-8914(34)80246-7

    work page doi:10.1016/s0031-8914(34)80246-7 1934

  41. [41]

    Nikulov, Dynamic processes in superconductors and the laws of thermodynamics, Physica C 589 (2021) 1353934

    A.V. Nikulov, Dynamic processes in superconductors and the laws of thermodynamics, Physica C 589 (2021) 1353934. https://doi.org/10.1016/j.physc.2021.1353934

    work page doi:10.1016/j.physc.2021.1353934 2021

  42. [42]

    Little, and R.D

    W.A. Little, and R.D. Parks, Observation of Quantum Periodicity in the Transition Temperature of a Super- conducting Cylinder, Phys. Rev. Lett. 9 (1962) 9. DOI: https://doi.org/10.1103/PhysRevLett.9.9

    work page doi:10.1103/physrevlett.9.9 1962

  43. [43]

    Koshnick, H

    N.C. Koshnick, H. Bluhm, M.E. Huber, and K.A. Moler, Fluctuation Superconductivity in Mesoscopic Aluminum Rings, Science 318 (2007) 1440-1443. DOI: https://doi.org/10.1126/science.1148758

    work page doi:10.1126/science.1148758 2007

  44. [44]

    A. A. Burlakov, V. L. Gurtovoi, S. V. Dubonos, A.V. Nikulov, and V.A. Tulin, Little-Parks Ef- fect in a System of Asymmetric Superconduct- ing Rings, JETP Lett. 86 (2007) 517-521. DOI: https://doi.org/10.1134/S0021364007200052

    work page doi:10.1134/s0021364007200052 2007

  45. [45]

    Gurtovoi, A.I

    V.L. Gurtovoi, A.I. Ilin, A.V. Nikulov, and V.A. Tulin, Weak dissipation does not result in disappearance of per- sistent current. Low Temp. Phys. 36 (2010) 974-981

    2010

  46. [46]

    V. L. Gurtovoi, M. Exarchos, V. N. Antonov, A. V. Nikulov and V. A. Tulin, Multiple superconduct- ing ring ratchets for ultrasensitive detection of non- equilibrium noises, Appl. Phys. Lett. 109 (2016) 032602. http://dx.doi.org/10.1063/1.4958731

    work page doi:10.1063/1.4958731 2016

  47. [47]

    Hirsch, Does the Meissner effect require radial charge flow? Physica C 633 (2025) 1354724

    J.E. Hirsch, Does the Meissner effect require radial charge flow? Physica C 633 (2025) 1354724. 18

    2025

  48. [48]

    Hirsch, Consequences of charge imbalance in super- conductors within the theory of hole superconductivity, Phys

    J.E. Hirsch, Consequences of charge imbalance in super- conductors within the theory of hole superconductivity, Phys. Lett. A 281 (2001) 44

    2001

  49. [49]

    Hirsch, The Lorentz force and superconductivity, Phys

    J.E. Hirsch, The Lorentz force and superconductivity, Phys. Lett. A 315 (2003) 474

    2003

  50. [50]

    Hirsch, On the dynamics of the Meissner effect, Phys

    J.E. Hirsch, On the dynamics of the Meissner effect, Phys. Scr. 91 (2016) 035801

    2016

  51. [51]

    Hirsch, Momentum of superconducting electrons and the explanation of the Meissner effect, Phys

    J.E. Hirsch, Momentum of superconducting electrons and the explanation of the Meissner effect, Phys. Rev. B 95 (2017) 014503

    2017

  52. [52]

    Hirsch, Explanation of the Meissner effect and pre- diction of a spin Meissner effect in low and high Tc su- perconductors, Physica C 470 (2010) S955

    J.E. Hirsch, Explanation of the Meissner effect and pre- diction of a spin Meissner effect in low and high Tc su- perconductors, Physica C 470 (2010) S955

    2010

  53. [53]

    Hirsch, How do supercurrents die down when a superconductor goes normal? Physica C 635 (2025) 1354747

    J.E. Hirsch, How do supercurrents die down when a superconductor goes normal? Physica C 635 (2025) 1354747

    2025

  54. [54]

    Deaver Jr

    B.S. Deaver Jr. and W.M. Fairbank Experimental Ev- idence for Quantized Flux in Superconducting Cy- clinders, Phys. Rev. Lett. 7 (1961) 43-46. DOI: https://doi.org/10.1103/PhysRevLett.7.43

    work page doi:10.1103/physrevlett.7.43 1961

  55. [55]

    Doll and M

    R. Doll and M. Nobauer, Experimental Proof of Magnetic Flux Quantization in a Superconduct- ing Ring, Phys. Rev. Lett. 7 (1961) 51-52. DOI: https://doi.org/10.1103/PhysRevLett.7.51

    work page doi:10.1103/physrevlett.7.51 1961

  56. [56]

    Landau, Theory of Superfluidity of Helium II, Zh.Eksp.Teor.Fiz

    L.D. Landau, Theory of Superfluidity of Helium II, Zh.Eksp.Teor.Fiz. 11 (1941) 592-623

    1941

  57. [57]

    Ginzburg and L.D

    V.L. Ginzburg and L.D. Landau, On the theory of super- conductivity, Zh. Eksp. Teor. Fiz. 20 (1950) 1064-1076

    1950

  58. [58]

    Abrikosov, On the magnetic properties of supercon- ductors of the second group

    A.A. Abrikosov, On the magnetic properties of supercon- ductors of the second group. Sov. Phys.-JETP 5 (1957) 1174-1182

    1957

  59. [59]

    V. L. Gurtovoi, S. V. Dubonos, A. V. Nikulov, N.N. Os- ipov, and V. A. Tulin, Dependence of the magnitude and direction of the persistent current on the magnetic flux in superconducting rings, JETP 105 (2007) 1157-1173. DOI: https://doi.org/10.1134/S1063776107120072

    work page doi:10.1134/s1063776107120072 2007

  60. [60]

    V. L. Gurtovoi and A. V. Nikulov, Comment on ”Vor- tices induced in a superconducting loop by asymmet- ric kinetic inductance and their detection in transport measurements”, Phys. Rev. B 90 (2014) 056501. DOI: https://doi.org/10.1103/PhysRevB.90.056501

    work page doi:10.1103/physrevb.90.056501 2014

  61. [61]

    Bleszynski-Jayich, W

    A.C. Bleszynski-Jayich, W. E. Shanks, B. Peaude- cerf, E. Ginossar, F. von Oppen, L. Glazman, and J.G.E. Harris, Persistent Currents in Normal Metal Rings, Science 326 (2009) 272-275. DOI: https://doi.org/10.1126/science.1178139

    work page doi:10.1126/science.1178139 2009

  62. [62]

    Bluhm, N.C

    H. Bluhm, N.C. Koshnick, Ju.A. Bert, M.E. Hu- ber, and K.A. Moler, Persistent Currents in Normal Metal Rings, Phys. Rev. Lett. 102 (2009) 136802. DOI: https://doi.org/10.1103/PhysRevLett.102.136802

    work page doi:10.1103/physrevlett.102.136802 2009

  63. [63]

    A.V. Nikulov, A problem with the conservation law ob- served in macroscopic quantum phenomena is a conse- quence of violation of the correspondence principle, Chi- nese Journal of Physics 92 (2024) 270-283

    2024

  64. [64]

    Gurtovoi, V.N

    V.L. Gurtovoi, V.N. Antonov, A.V. Nikulov, R.S. Shaikhaidarov, V.A. Tulin, Development of a Su- perconducting Differential Double Contour Interfer- ometer, Nano Lett. 17 (2017) 6516-6519. DOI: https://doi.org/10.1021/acs.nanolett.7b01602

    work page doi:10.1021/acs.nanolett.7b01602 2017

  65. [65]

    Eilenberger, Momentum Conservation, Time De- pendent Ginzburg Landau Equation and Paraconduc- tivity, Zeitschrift fur Physik 236 (1970) 1-13

    G. Eilenberger, Momentum Conservation, Time De- pendent Ginzburg Landau Equation and Paraconduc- tivity, Zeitschrift fur Physik 236 (1970) 1-13. DOI: https://doi.org/10.1007/BF01394878

    work page doi:10.1007/bf01394878 1970

  66. [66]

    W J Skocpol and M Tinkham, Fluctuations near super- conducting phase transitions. Rep. Prog. Phys. 38 (1975) 1049 DOI https://doi.org/10.1088/0034-4885/38/9/001

    work page doi:10.1088/0034-4885/38/9/001 1975

  67. [67]

    Feynman, R.B

    R.P. Feynman, R.B. Leighton, M. Sands, The Feynman Lectures on Physics. Addison-Wesley Publishing Com- pany, Reading, Massachusetts, 1963

    1963

  68. [68]

    Planck, Scientific Autobiography and Other Papers, Williams and Norgate LTD: London, UK, 1950

    M. Planck, Scientific Autobiography and Other Papers, Williams and Norgate LTD: London, UK, 1950

    1950

  69. [69]

    Nikulov, Quantum force in a superconductor, Phys

    A.V. Nikulov, Quantum force in a superconductor, Phys. Rev. B. 64 (2001) 012505

    2001

  70. [70]

    Nikulov, Reply to Comment on ”Quantum Force in a Superconductor”, arXiv: cond-mat/0304313 (2003)

    A.V. Nikulov, Reply to Comment on ”Quantum Force in a Superconductor”, arXiv: cond-mat/0304313 (2003)

    Pith/arXiv arXiv 2003

  71. [71]

    Nikulov, About perpetuum mobile without emotions, AIP Conf

    A. Nikulov, About perpetuum mobile without emotions, AIP Conf. Proc. 643 (2002) 207-212

    2002

  72. [72]

    Nikulov, The Meissner effect puz- zle and the quantum force in superconduc- tor, Phys

    A.V. Nikulov, The Meissner effect puz- zle and the quantum force in superconduc- tor, Phys. Lett. A 376 (2012) 3392-3397. https://doi.org/10.1016/j.physleta.2012.09.028

    work page doi:10.1016/j.physleta.2012.09.028 2012

  73. [73]

    Nikulov, Quantum limits to the second law and breach of symmetry

    A. Nikulov, Quantum limits to the second law and breach of symmetry. Invited Lecture at the Conference ”Fron- tiers of Quantum and Mesoscopic Thermodynamics” 26- 29 July 2004, Prague; arXiv: cond-mat/0505508 (2005)

    Pith/arXiv arXiv 2004

  74. [74]

    Nyquist, Thermal Agitation of Electric Charge in Con- ductors

    H. Nyquist, Thermal Agitation of Electric Charge in Con- ductors. Phys. Rev. 32 (1928) 110-113

    1928

  75. [75]

    Johnson, Thermal Agitation of Electricity in Con- ductors

    J.B. Johnson, Thermal Agitation of Electricity in Con- ductors. Phys. Rev. 32 (1928) 97-109

    1928

  76. [76]

    Nikulov and I.N

    A.V. Nikulov and I.N. Zhilyaev, The Little-Parks Effect in an Inhomogeneous Superconducting Ring, J. Low Temp. Phys. 112 (1998) 227-235. DOI: https://doi.org/10.1023/A:1022637832482

    work page doi:10.1023/a:1022637832482 1998

  77. [77]

    Berger, Case of thermodynamic failure in the Ginzburg-Landau approach to fluctuation superconduc- tivity, Phys

    J. Berger, Case of thermodynamic failure in the Ginzburg-Landau approach to fluctuation superconduc- tivity, Phys. Rev. B 109 (2024) 024501

    2024

  78. [78]

    and Nikulov, A.V

    Dubonos, S.V.; Kuznetsov, V.I. and Nikulov, A.V. Seg- ment of an Inhomogeneous Mesoscopic Loop as a DC Power Source. Proceedings of 10th International Sym- posium ”NANOSTRUCTURES: Physics and Technol- ogy”, St Petersburg: Ioffe Institute, 2002 p.350; arXiv: physics/0105059 (2001)

    Pith/arXiv arXiv 2002

  79. [79]

    Dubonos, V.I

    S.V. Dubonos, V.I. Kuznetsov, I. N. Zhilyaev, A.V. Nikulov, and A.A. Firsov, Observation of the external- ac-current-induced dc voltage proportional to the persis- tent current in superconducting loops, JETP Letters 77 (2003) 371-375. DOI: https://doi.org/10.1134/1.1581963

    work page doi:10.1134/1.1581963 2003

  80. [80]

    Burlakov, V.L

    A.A. Burlakov, V.L. Gurtovoi, A.I. Il’in, A.V. Nikulov, V.A. Tulin, Possibility of persistent volt- age observation in a system of asymmetric super- conducting rings, Phys. Lett. A 376 (2012) 2325. https://doi.org/10.1016/j.physleta.2012.04.032

    work page doi:10.1016/j.physleta.2012.04.032 2012

Showing first 80 references.