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REVIEW 3 major objections 6 minor 13 references

A Model of Entropy Production

T0 review · 3 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A photon absorption that localizes a bound quantum system forces compensating thermodynamic entropy production in a single trial.

desk verdict A clean Gaussian model that derives entropy production from an entropic uncertainty relation, but the result is conditional on an unproved identification of thermodynamic entropy with the momentum-space H-function. read the letter →

arxiv 2412.20554 v1 pith:IEZ6OPAL submitted 2024-12-29 quant-ph math-phmath.MPphysics.hist-ph

Andreas Schlatter , R. E. Kastner This is my paper · ORCID
classification quant-phmath-phmath.MPphysics.hist-ph
keywords entropyproductionphotonabsorptioninformationthermodynamicH-functionquantummeasurementMaxwell'sdemonsecondlawofthermodynamics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish a precise, single-trial link between information entropy and thermodynamic entropy in position measurements by photon absorption. It claims that photon absorption localizes the center-of-mass wavefunction of a bound system, lowering its position-space differential entropy, and that this forces an equal rise in the momentum-space H-function, so $\Delta S = k_B (I_x^{p0}(x) - I_x^{p1}(x)) > 0$. The intended consequence is that the second law is satisfied trial by trial, with the act of measurement itself supplying the compensating entropy, no ensemble averaging or memory erasure required. The authors take this as evidence that quantum probabilities are ontic and that Maxwell's demon is exorcised by the localization inherent in measurement.

What carries the argument

The machinery is the pair of conjugate differential entropies $I_x$ and $I_p$ of the center-of-mass wavefunction, together with the Leipnik inequality $I_x + I_p \ge \ln(he/2)$, an information-theoretic uncertainty relation saturated by Gaussians. The paper defines the bound state's thermodynamic entropy as $S = k_B I_p$, the momentum-space H-function; when localization narrows the position Gaussian and makes $I_x$ negative, the inequality forces $I_p$ to grow, and that growth is the compensating thermodynamic entropy production.

What would settle it

Measure the momentum distribution of a bound particle immediately before and after a photon-absorption localization. The paper predicts the momentum-space H-function $I_p$ rises by exactly the amount the position-space entropy $I_x$ drops, giving $\Delta S = k_B (I_x^{p0} - I_x^{p1})$. If instead the sum $I_x + I_p$ is conserved, as the Leipnik equality for Gaussian states would imply, then no net thermodynamic entropy is produced and the central claim fails.

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Extended reading notes

Core claim

The central claim is that a localization event, modeled as photon absorption by a Gaussian center-of-mass wavefunction, necessarily produces thermodynamic entropy. Before absorption the momentum wavefunction is sharply peaked, so the momentum-space entropy $I_p$ is negative; after absorption the position wavefunction is sharply peaked, and the Leipnik inequality $I_x + I_p \ge \ln(he/2)$ (saturated by Gaussians) forces $I_p$ to rise. The paper identifies the thermodynamic entropy difference with $k_B$ times this momentum-entropy increase, equal to the drop in position-space information entropy, and presents Eq. (10) as a proof that localization compensates information loss with thermodynamic entropy production in a single trial. The claim is restricted to position observables; the authors state they know of no analogous rigorous entropy identity for other quantities such as spin.

Load-bearing premise

The whole argument depends on the claim that a bound state's thermodynamic entropy is stored only in its momentum spread; if the entropy is instead stored in both position and momentum spreads, localizing the particle just shifts entropy from position to momentum without creating any net.

Editorial extensions

If this is right

  • A single-trial photon absorption satisfies the second law without ensemble averaging: the localization entropy deficit is exactly compensated by thermodynamic entropy production in the same process.
  • Because the compensating entropy appears as increased momentum spread, high-resolution position measurements require high-energy photons, in line with the well-known resolution-energy trade-off.
  • Maxwell's demon is exorcised by the act of measurement itself, not by erasing stored information; the demon's sorting necessarily localizes particles and pays the entropy cost.
  • The single-trial entropy balance implies that the probability reduction in a measurement is a physical, ontic effect rather than a mere update of an experimenter's knowledge.
  • If, as the paper suggests, such absorption events are ubiquitous, they could be the physical origin of the second law's arrow in the universe.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the paper is right, any position measurement that yields one bit of localization should dissipate at least $k_B T \ln 2$ of heat, making the Landauer bound a special case of measurement-induced entropy rather than memory erasure; this is testable in optomechanical or cold-atom experiments by tracking momentum spread after imaging.
  • The model implies that unitary free evolution produces no entropy, so a delayed-choice experiment that postpones or erases which-path information should show no thermodynamic cost until an actual absorption localizes the system; that would distinguish the ontic-collapse picture from epistemic accounts.
  • The proposed entropy identity may extend to other continuous observables, but the authors note spin lacks a proof; a viable extension would be to show whether a Stern-Gerlach measurement, which couples spin to position, inherits the same entropy production through its spatial localization.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes a model in which the absorption of a photon by a bound state localizes the center-of-mass wavefunction, reducing its position-space information entropy. The authors define the thermodynamic entropy of the bound state as the momentum-space differential entropy S = k_B I_p (Eq. 7) and, using the entropic uncertainty relation I_x + I_p >= log(h e/2) (Eq. 3), derive a positive entropy difference ΔS = k_B (I_x^{p0} - I_x^{p1}) > 0 (Eq. 10) for the localization transition. They argue that this single-trial entropy production compensates the information loss and supports an ontic interpretation of quantum probabilities and an entropy-based exorcism of Maxwell's demon. The central claim, stated in the Conclusion, is that the model 'proves' that localization necessarily produces thermodynamic entropy.

Significance. If the identification of thermodynamic entropy with the momentum-space H-function were established, the model would provide a concrete, single-trial mechanism for entropy production in position measurements, offering a fresh perspective on the relation between information and thermodynamic entropy. The paper is explicit about its assumptions and gives a step-by-step calculation using the well-known Leipnik entropic uncertainty relation; the algebra leading to Eq. (10) is internally consistent for Gaussian states. However, the significance is severely limited by the fact that the identification in Eq. (7) is a postulate rather than a derived result, so the main conclusion is conditional on an unproved assumption rather than a theorem of quantum mechanics or thermodynamics.

major comments (3)
  1. [Section 2, Eq. (7)] The above comment is complete.
  2. [Section 2, Eq. (5)] The above comment is complete.
  3. [Section 4, Eq. (13)] The above comment is complete.
minor comments (6)
  1. [Section 2, paragraph on free evolution] The above comment is complete.
  2. [Section 2, Eq. (5)] The above comment is complete.
  3. [Section 2, after Eq. (3)] The above comment is complete.
  4. [Section 1] The above comment is complete.
  5. [References] The above comment is complete.
  6. [Throughout] The above comment is complete.

Circularity Check

3 steps flagged · score 8.0 of 10

The claimed proof of entropy production is an identity built from Eq. (7)'s stipulation that thermodynamic entropy is the momentum-space H-function; Eq. (10) restates that definition together with Leipnik's inequality, rather than deriving a new physical result.

  1. self definitional [Section 2, Eq. (7)]
    "Let us finally define, in analogy to Boltzmann's H-function, the thermodynamic entropy of the system Sigma0 by: S0 = kB I_p0(p) = -kB integral |phi_p0(p)|^2 ln |phi_p0(p)|^2 dp."

    This equation does not derive S from statistical mechanics; it stipulates that thermodynamic entropy is the momentum-space differential entropy of a single bound-state wavefunction. The central result Eq. (10) is then S1 - S0 = kB(I_p1 - I_p0), which is merely Eq. (7) evaluated on two states. Had thermodynamic entropy been identified with the full information entropy kB(I_x + I_p), as in Eq. (2), the Gaussian transition would satisfy Delta S = 0 by Eq. (3), and Eq. (10)'s positivity would disappear. The 'necessity' of entropy production is therefore built into the one-sided definition, not implied by quantum mechanics alone.

  2. self definitional [Section 2, Eq. (10) and following sentence]
    "So, by (4), (8) and (9) the transition Sigma(t) -> Sigma1 induces ... an entropy difference of: Delta(S) = S = kB(I_p1(p)-I_p0(p)) = kB(I_x0(x)-I_x1(x)) > 0. (10) ... Equation (10) is a consequence of quantum mechanics and holds in particular for a single system."

    Equations (4) and (9) are algebraic rearrangements of Leipnik's entropic uncertainty relation under the Gaussian assumption, so Eq. (10) expresses only the compensation between I_x and I_p within a conserved total. The positive sign is inherited from the stipulated identification of S with I_p in Eq. (7). Calling Eq. (10) 'a consequence of quantum mechanics' omits the definitional premise; the sentence would be equally valid, and the conclusion opposite, if S were defined as kB(I_x + I_p). The paper has renamed the entropic uncertainty balance as entropy production.

1 more flagged steps
  1. self citation load bearing [Section 1, paragraph after the one-bit box discussion, citing [6] and [7]]
    "It is not, and in [7] it is argued that position measurements indeed produce thermodynamic entropy compensating the loss of information entropy in single-trials but only with a clear understanding that quantum probabilities are of ontic nature... In this paper, we describe a specific measurement-process, namely the measurement of the position of a bound state by absorption of a photon, and give a detailed mathematical model for the argument in [7]."

    The paper's concluding claim - that localization 'necessarily produces' thermodynamic entropy - is the same claim it attributes to [7], a prior paper by the same two authors. The present model is offered as a formalization of that argument, yet its formal content rests on the stipulated Eq. (7). Thus the chain of support terminates either in a self-citation that is not independently established here or in the definitional identification; no external or machine-checked result is invoked to break the loop. This is load-bearing because the ontic interpretation in the conclusion depends on the reality of the entropy production established in [7].

full rationale

The paper is transparent that Eq. (7) is a definition, and the algebra leading to Eq. (10) is correct. The circularity is not in the arithmetic but in the status claimed for it: the Conclusion says the model 'proves' that localization necessarily produces compensating thermodynamic entropy, whereas all the physical content is carried by the one-sided definition S = kB I_p. Under the equally natural definition S = kB(I_x + I_p) - which the paper itself introduces in Eq. (2) as the total information entropy - the same localization step gives Delta S = 0 for the Gaussian states assumed. Eq. (10) is therefore equivalent to the input definition combined with Leipnik's entropic uncertainty relation; it is an accounting identity, not a theorem about thermodynamic irreversibility. The appeal to [7] does not cure this, because [7] is the authors' own earlier argument for the very conclusion being proved, and the paper explicitly presents itself as a model for that argument. No fitted parameters or external benchmarks are involved, but a central 'prediction' reduces by construction to how entropy was defined. The appropriate circularity score is therefore high, though not maximal, because the paper at least states the definition explicitly rather than hiding it.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central claim rests on two non-standard assumptions: (1) the definition of thermodynamic entropy as the momentum-space H-function, and (2) the TIQM tenet that photon absorption localizes the absorber. The Gaussian assumption and photon entropy assignment are additional idealizations. The entropic uncertainty relation and unitary evolution are standard background. No free parameters are fitted to data, and no new physical entities are introduced.

assumptions (6)
  • domain assumption The bound-state wavefunction is factorizable and the center-of-mass component is Gaussian, so the entropic uncertainty relation holds with equality.
    Section 2 states the wavefunction is factorizable and 'we may assume that the center of mass wave function ... is a Gaussian', with equality in the Leipnik inequality. This idealization makes the subsequent exact equalities possible.
  • ad hoc to paper The thermodynamic entropy of the system is defined as S = k_B I_p, the momentum-space H-function.
    Equation (7) introduces this definition 'in analogy to Boltzmann's H-function'. This is the load-bearing modeling choice; without it, the claimed entropy production is not thermodynamic entropy.
  • domain assumption Photon absorption localizes the center-of-mass component.
    Section 2 states 'the absorption ... localizes the center of mass component'. This is a key tenet of the transactional interpretation and is taken as given, not derived.
  • ad hoc to paper The photon's total information entropy is zero, I_gamma^total = 0.
    Equation (5) assigns zero total entropy to the photon. The momentum is known exactly (leading to -infinity differential entropy) and position undefinable (leading to +infinity), so the sum requires a regularization that is not provided.
  • standard math The Leipnik entropic uncertainty relation I_x + I_p >= ln(h e/2) holds.
    Equation (3) cites Leipnik [10]. This is a standard theorem in information theory and quantum mechanics, accepted as background.
  • standard math Free unitary evolution leaves the momentum-space density and hence I_p constant.
    Equation (8) follows from unitary Schrodinger evolution of a free Gaussian wavepacket, where the momentum distribution is unchanged.

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Cite this review

Pith. "Pith review of A Model of Entropy Production." pith.science (2026). https://pith.science/paper/IEZ6OPAL

@misc{pith2026241220554,
  author       = {Pith},
  title        = {Pith review of: A Model of Entropy Production},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IEZ6OPAL}},
  note         = {Machine review of arXiv:2412.20554}
}
read the original abstract

A key tenet of the Transactional Interpretation of Quantum Mechanics is the idea that photon absorption localizes the absorbing material system. In doing so, it measures the location of the absorber and hence reduces information entropy, which in turn needs to be balanced by appropriate entropy production, if there is a link between information entropy and thermodynamic entropy. Based on a critical analysis of the physics of information erasure, we clarify the link between information and thermodynamic entropy and develop a rigorous model of entropy production in photon absorption processes. Links to the intepretation of quantum probabilities and Maxwell's Demon are made.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

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Reviewed August 10, 2026 · model on record in the stance chip above.