Maxwell's Demon

R. E. Kastner

arxiv: 2605.17196 · v1 · pith:HKHH6SULnew · submitted 2026-05-16 · 🪐 quant-ph · physics.data-an· physics.hist-ph

Maxwell's Demon

R. E. Kastner This is my paper

Pith reviewed 2026-05-20 13:53 UTC · model grok-4.3

classification 🪐 quant-ph physics.data-anphysics.hist-ph

keywords Maxwell's demonsecond law of thermodynamicsHeisenberg uncertainty principleLandauer's principlequantum thermodynamicsinformation and entropySzilard engine

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The pith

The Heisenberg uncertainty principle prevents Maxwell's demon from violating the second law.

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

This paper surveys the history of Maxwell's demon as an apparent loophole in the second law of thermodynamics, covering Maxwell's original sorting idea, Szilard's one-molecule engine, Brillouin's photon-based measurement argument, and Bennett's later emphasis on memory erasure costs. It then advances a new resolution: the Heisenberg uncertainty principle applied directly to the demon's measurement and control actions blocks the precise knowledge needed to extract work without an offsetting energy expenditure. This quantum limit also supplies an independent basis for Landauer's principle that the minimal cost of information processing is set by uncertainty rather than by computational steps alone.

Core claim

The paper claims that neglected features of quantum theory, in particular the Heisenberg uncertainty principle applied to the demon's hypothetical measurement and control operations, furnish a firm foundation for the second law by showing that the demon cannot obtain the information required for selective sorting without incurring an energy cost that restores thermodynamic balance.

What carries the argument

Direct application of the Heisenberg uncertainty principle to the demon's measurement and control operations

Load-bearing premise

The Heisenberg uncertainty principle can be applied directly to the demon's hypothetical measurement and control operations in a way that necessarily prevents violation of the second law without further modeling of quantum measurement details.

What would settle it

A concrete calculation or experiment in which a quantum-controlled system performs demon-like sorting or work extraction while keeping total energy dissipation below the uncertainty-derived minimum would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.17196 by R. E. Kastner.

**Figure 1.** Figure 1: The basic Szilard Engine setup Szilard did not propose a specific physical explanation for why the Demon should not be able to accomplish this apparent violation of the Second law; instead, he assumed, by reference to the Second Law, that the Demon must incur an entropy cost through the need to interact with the system to measure the atom’s position. However, at the classical level and assuming frictionles… view at source ↗

**Figure 2.** Figure 2: Gas molecule depicted as a localized classical particle [PITH_FULL_IMAGE:figures/full_fig_p024_2.png] view at source ↗

**Figure 3.** Figure 3: A real, delocalized quantum molecule Thus the placing of the partition is indeed crucially affecting its quantum state by confining it to a smaller volume. In effect, the partition insertion functions as a quantum measurement, where here the term “measurement” means an interaction resulting in a localization (reduction in uncertainty) of the system’s wavefunction ψ(x). Specifically, the molecule’s wavefunc… view at source ↗

read the original abstract

This work provides an overview of key historical developments in the formulation of the Second Law of Thermodynamics, focusing on the notorious challenge of ``Maxwell's Demon'', a hypothetical creature who could presumably violate that law. It begins by recalling Maxwell's challenge and discussing the apparent loophole in the Second Law that appears to make such a violation possible. An alternative formulation of the Demon challenge by Szilard is considered, along with his attempted defeat of the Demon through reference to measurement. A similar effort by Brillouin is also analyzed. The proposal of Bennett to defeat the Demon through the requirement of memory erasure is critically discussed. Finally, it is proposed that the Second Law gains a firm foundation through neglected features of quantum theory. In particular, an application of the Heisenberg Uncertainty Principle is shown to decisively defeat the Demon, as well as to serve as justification for Landauer's Principle, albeit in terms distinct from the usual computational formulation.

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.

Desk Editor's Note private letter to a colleague

Kastner reviews the Demon history and suggests the Uncertainty Principle defeats it plus grounds Landauer's principle without the usual computation angle, but the key step is asserted rather than derived.

read the letter

The main point to know is that this is a historical synthesis of Maxwell's Demon attempts followed by a proposal that the Heisenberg Uncertainty Principle can block any violation of the second law and support Landauer's principle in non-computational terms. The historical sections cover Maxwell's setup, Szilard's engine, Brillouin's measurement argument, and Bennett's memory-erasure fix, noting where each one falls short according to the author. That part reads cleanly and pulls the thread together without unnecessary detours. The proposed alternative using the Uncertainty Principle is the element the paper highlights as new, framing it as a direct quantum feature that prevents perfect control or erasure. The paper does well at keeping the discussion accessible for readers who want the background without chasing every original reference. The soft spot is the absence of any concrete model. The claim that the Uncertainty Principle decisively defeats the Demon requires showing how the relation imposes a specific entropy cost on the Demon's operations, yet the text supplies no interaction details, no probe state, and no calculation connecting the uncertainty bound to k ln 2 per bit. Without that step the argument stays at the level of suggestion rather than demonstration, which leaves the circularity concern open. This paper is mainly for people working on quantum foundations or the history of thermodynamics who already know the standard resolutions. A reader after new quantitative predictions or machine-checked results will not find them. It is worth sending to referees because the historical overview is reliable and the proposal raises a clear question that experts can test for rigor, even if substantial revision would be needed to make the central step hold up.

Referee Report

2 major / 2 minor

Summary. The paper reviews historical formulations of Maxwell's Demon and challenges to the Second Law, covering Maxwell's original thought experiment, Szilard's one-molecule engine, Brillouin's information-based resolution, and Bennett's memory-erasure argument. It then advances the central claim that an application of the Heisenberg Uncertainty Principle provides a decisive defeat of the Demon and an independent justification for Landauer's Principle, distinct from standard computational accounts.

Significance. A rigorously derived link between the uncertainty principle and a minimum thermodynamic cost for the Demon's operations would constitute a notable contribution by supplying a quantum-mechanical grounding for the Second Law that does not rely on information theory or erasure costs. The historical overview is competent, but the absence of explicit modeling limits the significance of the new proposal.

major comments (2)

[HUP application / proposal section] In the section presenting the HUP-based defeat of the Demon, no interaction Hamiltonian, probe state, or explicit calculation is supplied that converts the relation Δx Δp ≥ ħ/2 into a lower bound on entropy production of order k ln 2 per bit of information acquired or erased. Without this step the claim that the principle 'decisively defeats' the Demon remains an assertion rather than a derivation.
[HUP application / proposal section] The same HUP argument is invoked both to block the Demon's information gain and to justify Landauer's Principle. Because the thermodynamic cost is not independently derived from the uncertainty relation, the reasoning risks circularity: the principle is used to explain the very cost it is supposed to enforce.

minor comments (2)

[Proposal section] Notation for the uncertainty relation and for the Demon's 'measurement' is introduced without a preceding definition of the relevant operators or states, making the subsequent claims difficult to follow.
[Abstract] The abstract states that the HUP application is 'shown' to defeat the Demon; the body should either supply the missing derivation or qualify the claim as a conceptual suggestion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful review and for identifying areas where the presentation of our HUP-based proposal can be strengthened. The manuscript is primarily an overview with a conceptual suggestion rather than a full technical derivation; we address the specific concerns below and indicate where revisions will be made.

read point-by-point responses

Referee: In the section presenting the HUP-based defeat of the Demon, no interaction Hamiltonian, probe state, or explicit calculation is supplied that converts the relation Δx Δp ≥ ħ/2 into a lower bound on entropy production of order k ln 2 per bit of information acquired or erased. Without this step the claim that the principle 'decisively defeats' the Demon remains an assertion rather than a derivation.

Authors: We agree that the current text presents the link between the Heisenberg Uncertainty Principle and a thermodynamic cost at a conceptual level without supplying an explicit interaction Hamiltonian, probe state, or step-by-step calculation. The manuscript's aim is to highlight a quantum-mechanical grounding for the Second Law that is distinct from information-theoretic accounts, but we recognize that a more detailed derivation would make the claim more rigorous. In the revised version we will add a short subsection providing a heuristic argument: the position-momentum uncertainty implies that any measurement by the Demon disturbs the molecule's momentum by an amount sufficient to require compensatory work of order kT ln 2 to restore equilibrium, thereby producing entropy. A fully rigorous model with a concrete Hamiltonian is left for future work, as the paper is an overview rather than a technical derivation. revision: yes
Referee: The same HUP argument is invoked both to block the Demon's information gain and to justify Landauer's Principle. Because the thermodynamic cost is not independently derived from the uncertainty relation, the reasoning risks circularity: the principle is used to explain the very cost it is supposed to enforce.

Authors: We maintain that the reasoning is not circular. The HUP is applied first to the measurement act itself: any attempt to localize the molecule's position or velocity necessarily introduces an uncontrollable disturbance whose energy scale sets a minimum cost for information acquisition, independent of later erasure. The same principle is then invoked for memory reset because erasing the Demon's record requires reducing the uncertainty in its own state, again incurring a disturbance cost. This supplies a common quantum origin for both effects without presupposing the thermodynamic cost. To prevent any appearance of circularity we will revise the relevant paragraphs to separate the two applications more explicitly and to state that the cost follows directly from the measurement back-action implied by the uncertainty relation rather than from an assumed Landauer bound. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claim presented as independent quantum-theoretic application

full rationale

The paper's abstract and overview frame the defeat of Maxwell's Demon and justification of Landauer's Principle as arising from an application of the Heisenberg Uncertainty Principle drawn from neglected features of quantum theory, presented in terms distinct from computational formulations. No equations, fitted parameters, self-citations, or ansatzes are quoted that reduce the claimed result to the inputs by construction. The derivation chain is therefore treated as self-contained against external benchmarks, with any concerns about explicit modeling or interaction Hamiltonians falling under correctness rather than circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard quantum mechanics applied to a thought experiment, with no new free parameters, invented entities, or ad-hoc axioms introduced beyond the domain assumption that the Uncertainty Principle governs the Demon's operations.

axioms (1)

domain assumption The Heisenberg Uncertainty Principle applies directly to the Demon's measurement and control actions in a way that prevents net violation of the Second Law.
Invoked in the abstract as the decisive mechanism that defeats the Demon and grounds Landauer's Principle.

pith-pipeline@v0.9.0 · 5675 in / 1322 out tokens · 73460 ms · 2026-05-20T13:53:29.291454+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

I(x, p) = −∫ |ψ(x)|² ln|ψ(x)|² dx − ∫ |ϕ(p)|² ln|ϕ(p)|² dp ≥ ln(ℏe/2); S = k I(p) yields ΔS = k ln 2 upon localization
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean J_uniquely_calibrated_via_higher_derivative echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

reduction in position uncertainty forces conjugate momentum spread and therefore entropy increase independent of observer knowledge

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

9 extracted references · 9 canonical work pages

[1]

Are there quantum jumps?

Bell, J.S. (1987). “Are there quantum jumps?” In Kilmister, Ed.Schrodinger: Century of a Polymath, p

work page 1987
[2]

Logical Reversibility of Computation,

Cambridge: Cambridge University Press. Bennett, C. (1973) “Logical Reversibility of Computation,” IBM Journal of Research and Development 17, 525–532. Bennett, C. (1982) “The Thermodynamics of Computation: A Review,” International Journal of Theoretical Physics 21, 905–940. Bennett, C. (1987) “Demons, Engines, and the Second Law,”Scientific American 257, ...

work page 1973
[3]

In Christopher Hitchcock & Alan Hajek, edi- tors: Oxford Handbook of Probability and Philosophy , Oxford University Press, pp

Einstein, A. (1905a). ” ¨Uber die von der molekularkinetischen Theorie der W¨ arme geforderte Bewegung von in ruhenden Fl¨ ussigkeiten suspendierten Teilchen”. Annalen der Physik (in German). 322 (8): 549–560 Einstein, A. (1905b). Uber einen die Erzeugung and Verwandlung des Lichtes betre- ffenden heuristischen Gesichtspunkt. Annalen der Physik, 17, 132–1...

work page doi:10.1093/oxfordhb/9780199935314.013.63 1916
[4]

Maxwell’s Demon Is Foiled by the Entropy Cost of Measurement, Not Erasure,

Kastner, R. E. (2025) “Maxwell’s Demon Is Foiled by the Entropy Cost of Measurement, Not Erasure,”Foundations5(2),

work page 2025
[5]

The connection be- tween logical and thermodynamic irreversibility,

https://www.mdpi.com/2673-9321/5/2/16 Ladyman, J., Presnell, S., Short, A.J. and Groisman, B. (2007). “The connection be- tween logical and thermodynamic irreversibility,” Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics 38, 58–79. Lamb, W. and Retherford, R. (1947). “Fine Structure of the Hydrogen A...

work page 2007
[6]

Landau, L. D. and Lifshitz, E. M. (1980) Statistical Physics Part 1, Course in Theoretical Physics vol

work page 1980
[7]

Irreversibility and Heat Generation in the Computing Process,

3rd ed. Trans: J. B. Sykes and M. J. Kearsley. Oxford: Butterworth- Heinemann. Landauer, R. (1961) “Irreversibility and Heat Generation in the Computing Process,” IBM Journal of Research and Development 3, 183–191. Lanford, O. E. (1976). “On the derivation of the Boltzmann equation,” Asterisque 40, 117-137. Leff, H. S. and Rex, A. (2003) Maxwell’s Demon 2...

work page 1961
[8]

The (absence of a) relationship between thermodynamic and logical reversibility,

Maroney, O. (2005). “The (absence of a) relationship between thermodynamic and logical reversibility,” Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36, 355–374 (2005). Maroney, O. (2009) “Information Processing and Thermodynamic Entropy,” The Stanford Encyclopedia of Philosophy (Winter 2008 Editi...

work page 2005
[9]

On the Decrease of Entropy of a Thermodynamic System by the Intervention of an Intelligent Being,

Schrodinger, E. (1929).Science, Theory, and Man.(German edition; English translation published 1957). Schrodinger, E. (1957).Statistical Thermodynamics. Cambridge: Cambridge University Press. Schlatter, A., Kastner, R.E. (2024) A model of entropy production. Sci Rep 14, 30853. https://doi.org/10.1038/s41598-024-81671-w. Shannon, Claude E. (July 1948). ”A ...

work page doi:10.1038/s41598-024-81671-w 1929

[1] [1]

Are there quantum jumps?

Bell, J.S. (1987). “Are there quantum jumps?” In Kilmister, Ed.Schrodinger: Century of a Polymath, p

work page 1987

[2] [2]

Logical Reversibility of Computation,

Cambridge: Cambridge University Press. Bennett, C. (1973) “Logical Reversibility of Computation,” IBM Journal of Research and Development 17, 525–532. Bennett, C. (1982) “The Thermodynamics of Computation: A Review,” International Journal of Theoretical Physics 21, 905–940. Bennett, C. (1987) “Demons, Engines, and the Second Law,”Scientific American 257, ...

work page 1973

[3] [3]

In Christopher Hitchcock & Alan Hajek, edi- tors: Oxford Handbook of Probability and Philosophy , Oxford University Press, pp

Einstein, A. (1905a). ” ¨Uber die von der molekularkinetischen Theorie der W¨ arme geforderte Bewegung von in ruhenden Fl¨ ussigkeiten suspendierten Teilchen”. Annalen der Physik (in German). 322 (8): 549–560 Einstein, A. (1905b). Uber einen die Erzeugung and Verwandlung des Lichtes betre- ffenden heuristischen Gesichtspunkt. Annalen der Physik, 17, 132–1...

work page doi:10.1093/oxfordhb/9780199935314.013.63 1916

[4] [4]

Maxwell’s Demon Is Foiled by the Entropy Cost of Measurement, Not Erasure,

Kastner, R. E. (2025) “Maxwell’s Demon Is Foiled by the Entropy Cost of Measurement, Not Erasure,”Foundations5(2),

work page 2025

[5] [5]

The connection be- tween logical and thermodynamic irreversibility,

https://www.mdpi.com/2673-9321/5/2/16 Ladyman, J., Presnell, S., Short, A.J. and Groisman, B. (2007). “The connection be- tween logical and thermodynamic irreversibility,” Studies In History and Philosophy of Science Part B: Studies In History and Philosophy of Modern Physics 38, 58–79. Lamb, W. and Retherford, R. (1947). “Fine Structure of the Hydrogen A...

work page 2007

[6] [6]

Landau, L. D. and Lifshitz, E. M. (1980) Statistical Physics Part 1, Course in Theoretical Physics vol

work page 1980

[7] [7]

Irreversibility and Heat Generation in the Computing Process,

3rd ed. Trans: J. B. Sykes and M. J. Kearsley. Oxford: Butterworth- Heinemann. Landauer, R. (1961) “Irreversibility and Heat Generation in the Computing Process,” IBM Journal of Research and Development 3, 183–191. Lanford, O. E. (1976). “On the derivation of the Boltzmann equation,” Asterisque 40, 117-137. Leff, H. S. and Rex, A. (2003) Maxwell’s Demon 2...

work page 1961

[8] [8]

The (absence of a) relationship between thermodynamic and logical reversibility,

Maroney, O. (2005). “The (absence of a) relationship between thermodynamic and logical reversibility,” Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36, 355–374 (2005). Maroney, O. (2009) “Information Processing and Thermodynamic Entropy,” The Stanford Encyclopedia of Philosophy (Winter 2008 Editi...

work page 2005

[9] [9]

On the Decrease of Entropy of a Thermodynamic System by the Intervention of an Intelligent Being,

Schrodinger, E. (1929).Science, Theory, and Man.(German edition; English translation published 1957). Schrodinger, E. (1957).Statistical Thermodynamics. Cambridge: Cambridge University Press. Schlatter, A., Kastner, R.E. (2024) A model of entropy production. Sci Rep 14, 30853. https://doi.org/10.1038/s41598-024-81671-w. Shannon, Claude E. (July 1948). ”A ...

work page doi:10.1038/s41598-024-81671-w 1929