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REVIEW 3 major objections 6 minor 121 references

Energy and information: a chronicle of hesitations on the role of the observer in physics

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper argues that Landauer's principle—erasing one bit of data costs at least $T\ln 2$ of heat—is not a fundamental law, because erasure can be thermodynamically reversible under the right knowledge and control.

desk verdict A useful historical essay on the observer in thermodynamics, but the central claim that Landauer's principle is not a law is not backed by a closed-cycle counterexample. read the letter →

arxiv 2509.06957 v1 pith:5KHRGECI submitted 2025-05-26 physics.hist-ph cond-mat.stat-mech

Didier Lairez This is my paper · ORCID
classification physics.hist-phcond-mat.stat-mech PACS 05.70.-a89.70.Cf
keywords LandauerprinciplethermodynamicreversibilityobserverdependenceShannonentropyMaxwell'sdemonGibbsparadoxinformationisphysicaldata-bitversus
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

The paper tells the history of the link between energy and information as an oscillation between two views: that objective reality is what exists without an observer, and that it is what an observer can interact with. It argues that thermodynamics has always been observer-dependent, that statistical mechanics tried to escape this but failed, and that Shannon information theory and then Landauer's principle were further attempts to make the link look intrinsic. The paper's own contribution is the last step: it claims Landauer's principle is not a fundamental law. The reason is that erasing a data-bit need not cost a minimum heat of $T\ln 2$; whether the erasure is thermodynamically reversible depends on whether the initial bit value is known and on the control protocol used, and at least one protocol erases known or unknown bits quasistatically. If right, the celebrated energy cost of forgetting is an observer- and implementation-dependent statement, not a law of physics.

What carries the argument

The central mechanism is the distinction between a data-bit and a piece of information. A data-bit is a material system with two distinguishable stationary states; a piece of information is an abstract value that is not localized in any copy, so erasing one data-bit does not itself destroy information unless no copy remains. On top of this, the argument uses the Clausius inequality as the criterion of thermodynamic reversibility, applied to concrete implementations of a bit: the particle-in-a-box used by Landauer, and the paper's alternative of a particle on a fixed repulsive topographic relief driven by a single time-varying external field. In Landauer's derivation, erasure is free expansion followed by isothermal compression, and the merging of two paths is treated as necessarily uncontrolled; the paper's counterexample replaces that step by a controlled merging in which two initial trajectories can be quasistatically steered to the same final state. The known/unknown distinction does the final work: the first step of Landauer erasure is reversible for an unknown bit value and irreversible for a known one, so no intrinsic minimum heat cost follows for erasure as such.

What would settle it

For the paper's Figure 10 setup, write an explicit potential and drive schedule, then measure or simulate the dissipated heat as the drive speed tends to zero. If for either initial bit value the quasistatic heat fails to go to zero—or if the two trajectories cannot merge without passing through an unstable point where control is lost—the counterexample fails and the Landauer bound survives. A numerical simulation of overdamped Langevin dynamics with the explicit landscape would settle the question.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that Landauer's erasure principle is not a fundamental law of physics. The author distinguishes a piece of information, an abstract value that can be copied and is not located in any physical support, from a data-bit, a material system whose erasure is a thermodynamic process. Judged by the Clausius inequality, the thermodynamic reversibility of erasure depends on whether the initial value is known to the observer and on which control protocol is used, not on the fact that the logical operation 'set to 0' is non-injective. For an unknown initial value, the two-step Landauer erasure is thermodynamically reversible when the full restore cycle is included; for a known value it is irreversible, but an alternative procedure—a single time-varying external field acting on a particle in a fixed potential landscape—can erase either value quasistatically. Hence the inequality $W_{\mathrm{erase}}\ge T\ln 2$ does not express an intrinsic energy cost of forgetting; it characterizes a particular class of procedures and a particular observer. The same data-bit/information distinction is used to reject the information-mass equivalence that some authors present as a consequence of Landauer's principle.

Load-bearing premise

The load-bearing premise is that a single smoothly varied external field, acting on a particle in a fixed repulsive potential, can bring both possible starting positions to the same final position along paths whose heat dissipation can be made arbitrarily small by slowing the drive.

Editorial extensions

If this is right

  • The bound $W_{\mathrm{erase}}\ge T\ln 2$ would be demoted from a universal law to a statement about specific erasure protocols, valid when the protocol and the observer's knowledge make the process irreversible.
  • The information-mass equivalence, which is derived from Landauer erasure in the literature, would lose its foundation, since erasure need not dissipate and a data-bit need not store information.
  • Brillouin's negentropy principle would remain standing: acquiring one bit of information still costs at least $T\ln 2$ of work through the Clausius inequality, but the cost is a property of the whole acquisition cycle, not of the erasure step.
  • Any claimed experimental measurement of the Landauer bound would have to specify the initial knowledge about the bit and the full control protocol before the result can be attributed to 'erasure' rather than to the chosen implementation.

Reading between the lines

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

  • Editorial inference: if the paper is right, existing measurements reported as tests of the Landauer bound may actually be measuring a chosen protocol plus the experimenter's state of knowledge, so the same physical memory could show a $T\ln 2$ cost in one arrangement and zero in another.
  • Editorial inference: a direct next step would be to build an explicit topographic-relief potential and drive schedule—for example with a colloidal particle in an optical or magnetic trap—and check in the slow-drive limit that the dissipated heat approaches zero for both initial bit values.
  • Editorial inference: taken further, the data-bit/information distinction suggests that 'destroying information' is a global property of the whole memory (all copies gone), while local operations on a single data-bit can always be made reversible; this reframes the thermodynamics of computation away from logical non-injectivity and toward actual dissipative mechanisms.
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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 is a history-and-philosophy essay that traces the role of the observer in the energy-information link from classical thermodynamics through statistical mechanics, Shannon information theory, and Landauer's principle. Its central thesis is that thermodynamics is inherently observer-dependent, that information is a non-material abstraction stored in material data-bits, and that Landauer's principle is not a fundamental law of physics. The concrete invalidation claim is made in Section V: for an unknown initial bit value, the two-step Landauer erasure followed by a restore cycle is said to be thermodynamically reversible (Section V.E), and a single externally controlled time-varying field acting on a particle in a fixed repulsive potential is said to allow quasistatic erasure of either known or unknown bits (Section V.F.2, Fig. 10). The paper also critiques information-mass equivalence arguments.

Significance. If the invalidation of Landauer's principle were established, the paper would make a significant contribution to a long-standing debate in the foundations of thermodynamics and computation. The essay has genuine strengths: the historical narrative is readable, the free-expansion and Gibbs-paradox examples are presented clearly, the distinction between a piece of information and its data-bit support (Section V.A) is useful, and the observation that logical irreversibility and thermodynamic irreversibility are not the same thing (Section V.B) is supported by Maroney and Bennett. The paper also correctly identifies the shift of dissipation location in Brillouin versus Landauer formulations. However, the central counterexample is only sketched; no explicit potential, control schedule, work-heat bookkeeping, or closed-cycle proof is given. The significance of the paper is therefore conditional on the authors supplying a concrete, self-contained model of a zero-cost erasure cycle.

major comments (3)
  1. [V.F.2 and Fig. 10] The decisive counterexample is asserted rather than demonstrated. The text states that 'the motion of the particle follows the direction of maximum potential descent and can be as slow as desired,' but it does not specify the potential U(x), the time-dependent external field, the control schedule lambda(t), or the final reset procedure. This is load-bearing: in a genuinely quasistatic isothermal process the system is in equilibrium at every instant, so if the control is reset to the initial symmetric configuration the final equilibrium distribution is again 50/50 and the bit is not erased; if the control is not reset, the memory is not in its standard reusable configuration and the work and heat needed to restore the control must be included in the cycle balance. The paper needs a complete closed-cycle model with explicit U(x) and lambda(t), together with a proof that the protocol ends in state 0 with the control restored and with dissipated work going to zero in the quasistatic limit, before the claim 'Landauer is not a law' can be evaluated.
  2. [V.E and Figs. 8-9] The 'reversible Landauer erasure for an unknown value' is not an erasure. The protocol's steps 3 and 4 restore the data-bit to a random unknown value, so the complete cycle maps the initial 50/50 distribution to itself; it does not set the bit to state 0. A zero-cost cycle that erases a bit and then recreates it does not show that erasure itself has zero cost. The text concedes this when it says 'the thermodynamic cycle is not yet closed' and adds restore steps. To refute Landauer, the paper must exhibit a protocol that starts from an unknown bit (0 or 1) and ends with a known 0, with the control returned to its initial value, and with dissipated work below kT ln2 in the quasistatic limit. As written, Section V.E establishes only that a particular no-op cycle is reversible, which is not the same as reversible erasure.
  3. [V.F.1 and references [87, 90, 91]] The alternative erasure counterexamples are delegated to the author's own prior papers without a self-contained derivation. Section V.F.1 says 'counter-examples to the generality of Landauer erasure have been proposed [90, 91]' and then describes the scheme in one sentence; Section V.F.2's scheme is also a sketch. Since the conclusion that Landauer's principle is not a fundamental law rests entirely on these counterexamples, the manuscript should present the actual model, potential, and thermodynamic bookkeeping in enough detail for the reader to check the claim, or explicitly state the assumptions and provide a verifiable supplement. Citations to the author's own earlier work are not sufficient for a claim that overturns a widely accepted principle.
minor comments (6)
  1. [I.C.1] The free-expansion example is used as a foundational illustration of observer dependence, but the manuscript does not engage with the standard objection that thermodynamics defines macroscopic states by the values of state variables, not by the observer's state of knowledge. A sentence acknowledging this alternative reading would help the reader locate the paper's operationalist commitments.
  2. [II.D] The claim that the usual resolutions of the second Gibbs paradox 'benefit from the cancellation of two approximations' and that the exact Stirling formula changes the result is delegated to reference [55] without a derivation; since this point is not central to the main argument, a brief statement of the corrected result would improve readability.
  3. [Fig. 10 caption] The caption says 'the same time-varying tilt of the surface relative to the field' but does not define the parameter that is time-dependent or how it is reset. Clarifying the control schedule would make the figure self-contained.
  4. [III.A] The sentence 'since m(x)=n=2^log2 n, x requires log2(n) bits to be recorded' is notationally confusing; it should say that the outcome x is encoded by the integer n, whose binary representation requires roughly log2(n) bits.
  5. [V.A] The statement 'Both must be erased so that the information is irretrievably destroyed' should be qualified as 'both must be erased and no other copy may exist elsewhere,' since the previous paragraph already makes this point but the sentence as written could be read as claiming that two copies are always both necessary.
  6. [References] There is a typo in the van Kampen quotation, 'The choise,' and the paper uses 'textquote' markup artifacts in the abstract; these should be cleaned up, and the reference list should be checked for consistency of author names and formatting.

Circularity Check

3 steps flagged · score 6.0 of 10

The purported invalidation of Landauer's principle is partly circular: the decisive quasistatic-erasure counterexamples are imported from the author's own prior papers ([87], [90], [91]), and the 'reversible erasure' in Section V.E is a cycle that returns the bit to random, so its zero heat balance is built in rather than derived.

  1. self citation load bearing [Section V.F.2, 'Managing two possibilities with a single externally imposed procedure', and Fig. 10]
    "It can be an externally applied time-varying field, that exerts on a particle in a fixed and constant short range potential landscape, which can be viewed as a topographic relief [87]. ... Figure 10 gives an example of implementation. The motion of the particle follows the direction of maximum potential descent and can be as slow as desired."

    The decisive counterexample to Landauer's principle—that one externally controlled time-varying field plus a fixed repulsive landscape can merge the 0 and 1 trajectories quasistatically and erase a bit at zero cost—is not constructed in this paper. The only support for the mechanism is the author's own prior paper [87], whose title already asserts the conclusion ('why Landauer's result cannot be a physical principle'). No potential U(x), no control schedule lambda(t), and no proof that the merged trajectories avoid dissipation are given; 'can be as slow as desired' is an assertion. Thus the central invalidation reduces to an unverified self-citation chain.

  2. self citation load bearing [Section V.F.1, 'States incompletely defined for thermodynamics']
    "Based on this, counter-examples to the generality of Landauer erasure have been proposed [90, 91]. Basically, they work like that: the logical value of the data-bit is evaluated on the basis of a greatest quantity of information than that needed to describe the thermodynamic state. Typically, one single thermodynamic state can correspond to two distinct logical states. Then, there is absolutely no impediment for the erasure to be quasistatic."

    The alleged counterexamples are [90] and [91], both by the same author as the present paper. The text only summarizes their conclusion ('one single thermodynamic state can correspond to two distinct logical states ... there is absolutely no impediment for the erasure to be quasistatic') without supplying the construction, states, or energy balance in this manuscript. The claim that Landauer's principle fails in general is therefore load-bearing on the author's own prior papers rather than on a derivation reproduced here.

1 more flagged steps
  1. self definitional [Section V.E, 'On the thermodynamic reversibility of Landauer erasure' (steps 3-4)]
    "3. From state 0 to state S: use the piston that is already in position to do an isothermal expansion (i.e. reverse step 2 of Landauer erasure). 4. From state S to unknown-state: put back the partition, so that the final state is random and unknown. The energy exchanged during the step 3 compensates exactly that of step 2, so that the net balance is 0. Step 4 puts the data-bit at a random unknown value exactly as it was before. The Landauer erasure for an unknown value is thermodynamically reversible."

    The operation whose reversibility is demonstrated is erasure (steps 1-2, ending at state 0) followed by its exact reverse (step 3) and by reinsertion of the partition (step 4), ending at the original random state. The paper's own definition of erasure (Section IV.A item 2) is 'setting the bit-value to state 0'; after step 4 the bit is not set to 0. The zero net heat is true of a closed cycle by construction, so calling the combined loop 'Landauer erasure' makes the reversibility verdict an artifact of redefinition rather than a property of the erasure operation.

full rationale

The paper is a historical-philosophical essay with independent content: it quotes Bennett and Maroney for the known/unknown distinction and analyzes Landauer's derivation items on their own terms. However, the strongest version of the central claim—that Landauer's principle is not a law because a single fixed topography plus time-varying field can erase either a known or an unknown bit quasistatically—is not derived in this manuscript. Section V.F.2 imports the mechanism from the author's prior paper [87] (a paper whose title already states the conclusion), and Section V.F.1 imports the 'incomplete thermodynamic states' counterexamples from [90,91], also by the same author. None of these constructions, potentials, control schedules, or dissipation estimates is reproduced or machine-checked here. Section V.E's 'reversible erasure' is a closed cycle that restores the bit to random, so its zero net heat follows by construction and the operation is not erasure under the paper's own definition. The exact-Stirling correction [55] is a further self-citation but is less central. This is partial circularity (score 6): the thesis is not entirely self-referential because Bennett's acknowledged distinction gives some independent support, but the decisive constructive invalidation reduces to a self-citation chain and to a definitional re-labeling of a cycle as an erasure.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The paper makes no numerical fits and introduces no new physical entities. It rests on a set of philosophical and modeling assumptions, listed above, which carry most of the epistemic weight. The most fragile is the quasistatic-merging-path assumption behind the central counterexample.

assumptions (4)
  • ad hoc to paper Energy is defined only by a conservation principle whose list of forms is permanently open; anything that appears in a non-zero energy balance must be added to that list.
    Sec. I.A and I.D use this to conclude that information is a form of energy; it is the author's epistemological framing, not a theorem or experimental result.
  • domain assumption Thermodynamic reversibility is judged by the Clausius inequality and depends on the observer's knowledge of the initial state.
    Sec. I.C and V.E; this operationalist position is attributed to Gibbs and van Kampen and is the pivot for the known/unknown erasure argument.
  • ad hoc to paper Information is a non-material abstraction, distinct from its data-bit support, and is never located on a particular physical object.
    Sec. V.A and V.B; this distinction is asserted with dictionary definitions and examples and is load-bearing for the claim that information loss is independent of thermodynamic irreversibility.
  • ad hoc to paper A single externally controlled time-varying field, combined with a fixed internal topographic relief, can guide two different initial states to one final state along a quasistatic thermodynamic path.
    Sec. V.F.2 and Fig. 10; this is the premise of the decisive counterexample, asserted but not derived.

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Cite this review

Pith. "Pith review of Energy and information: a chronicle of hesitations on the role of the observer in physics." pith.science (2026). https://pith.science/paper/5KHRGECI

@misc{pith2026250906957,
  author       = {Pith},
  title        = {Pith review of: Energy and information: a chronicle of hesitations on the role of the observer in physics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5KHRGECI}},
  note         = {Machine review of arXiv:2509.06957}
}
read the original abstract

Energy has no definition, except that given by a conservation principle which essentially amounts to defining it as the elements of an open list of unknown cardinality. Entropy, identified by Shannon as information we lack, has too many definitions. This results in an unstable and hesitant interpretation of their link. Thermodynamics, the science of changes in form of energy, is phenomenological, all its laws are induced from observation. From the origin, the concept of energy is linked to the observer's knowledge, to the information he has: what and where to look and with what instruments. Thermodynamics only addresses the sensible world. It is Aristotelian. But this is disturbing if we consider that reason can give us access to Plato's intelligible world, the one that is beyond the sensible world and independent of us. This is disturbing if we consider that science can access to the intrinsic properties of things, those which are independent of us. This is disturbing if we have a purely Platonic conception of science. Hence the statistical mechanics approach ("The rational foundation of thermodynamics", J.W. Gibbs). This is the first pendulum movement of ideas, whose oscillations continue to this day, because unfortunately statistical mechanics introduces many inconsistencies, mainly due to the ergodic hypothesis. Luckily, these inconsistencies are all solved by Shannon's information theory. Sadly, information theory is too Aristotelian and too conceptual. Fortunately, Landauer principle makes it more \textquote{physical}. This is currently the latest attempt to bringing the notions of energy and information back to what is considered the right side of science, that of Plato. Landauer principle is now commonly regarded as a fundamental law of physics. Unpleasantly, it can be shown that this principle is not one.

Figures

Figures reproduced from arXiv: 2509.06957 by the authors.

Figure 1
Figure 1. FIG. 1. Road-map of the paper: submitted to two alternating [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Principle of conservation: energy is the thing that [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Top: joining two volumes of which we have no in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: FIG. 4. A large reservoir contains a gas. In the left side [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. An example of derivation of Gibbs and Boltzmann [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Landauer erasure: according to Landauer, the junc [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Landauer erasure of a data-bit represented by a single [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Landauer erasure of a data-bit: in case the initial [PITH_FULL_IMAGE:figures/full_fig_p018_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Data-bit materialized by a particle in a topographic [PITH_FULL_IMAGE:figures/full_fig_p019_10.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

121 extracted references · 66 canonical work pages

  1. [1]

    Is there a way, free from anya prioriconnection to thermodynamics, to derive a formula for entropy that allows us to define it ?

  2. [2]

    Is there a way, free from anya prioriconnection to thermodynamics, to predict the time evolution of a dynamical system of particles ?

  3. [3]

    Is there a way to define equilibrium not only as stationary (as in thermodynamics) but also as the stable state ? These three questions are closely related and it is im- portant to realize that they are absent from phenomeno- logical thermodynamics, but only introduced by statis- tical mechanics. 1) In phenomenological thermodynam- ics, there is no need o...

  4. [4]

    At some point or another, thermodynamics will come into play in the derivation

    Gibbs and Boltzmann Entropies Is there a way, free from anya prioriconnection to thermodynamics, to derive a formula for entropy that al- lows us to define it ? The answer is no. At some point or another, thermodynamics will come into play in the derivation. Figure 6 gives the outline of an example of derivation [33], other examples of derivation can be f...

  5. [5]

    molecular chaos

    Towards equilibrium and H-theorem Is there a way, free from anya prioriconnection to thermodynamics, to predict the time evolution of a dy- namical system of particles ? This question is implicitly related to entropy and to the Clausius inequality (Eq. 2). If a spontaneous change of an isolated system towards an equilibrium state corresponds in the end to...

  6. [6]

    undistinguishability

    The paradox of the stability of equilibrium Probabilities introduce fluctuations. A system at equi- librium is stationary on average, but may transiently de- viate from equilibrium. It is therefore imperative to in- troduce something into the theory, an additional postu- late or principle, that would play the role of an internal restoring force. Otherwise...

  7. [7]

    Negentropie principle of information

    concerns a system about which we are supposed to have all the information. •Shannon statistical entropy (Eq. 20 and 21) gives the same formula than Boltzmann or Gibbs, but probabilities have not the same meaning. They al- lows us to account for the actual information we have, or the information we consider relevant [17]. With information theory, we can co...

  8. [8]

    a particle in a bistable potential or a particle in a box divided in two

    The concrete implementation of a bit of memory is necessarily achieved via a physical system which must exhibit two stable thermodynamic states of equilibrium denoted 0 and 1, e.g. a particle in a bistable potential or a particle in a box divided in two

Show all 121 references
  1. [9]

    The procedure for erasing (the erasure) a bit of memory, say setting the bit-value to state 0, must be independent of its initial value (0 or 1), because it must be able to work for an unknown value

  2. [10]

    The two different paths that take the bit from state 0 or from state 1 to state 0 necessarily merge into one, at a point (called state S) where the value of the bit is undetermined. Before this point, both paths are judged necessarily uncontrolled and ther- modynamically irrev...

  3. [11]

    2 or 4), the subsequent step, from state S to state 0, necessarily 15 requires at leastTln 2 of work that will be dissi- pated as heat in the surroundings

    According to Clausius inequality (Eq. 2 or 4), the subsequent step, from state S to state 0, necessarily 15 requires at leastTln 2 of work that will be dissi- pated as heat in the surroundings. The first step (item 3) is similar to the free expansion of a gas while the second ...

  4. [12]

    The Landauer principle is one of the cornerstone of the modern theory of information

    from the 2nd law of thermodynamics and from the Clausius inequality, which have been confirmed by all known experiments; and 2) from two mathematical re- sults: Gibbs’s and Shannon’s ones. Since mathematical results are demonstrations that are not affected by the problem of in...

    1929

  5. [13]

    We shall call a device logically irreversible if the output of a device does not uniquely define the inputs

    At first,“We shall call a device logically irreversible if the output of a device does not uniquely define the inputs”[73].“[erase] is an example of a logical truth function which we shall call irreversible”[73]. Which means that “logically irreversible” functions applied to a...

  6. [14]

    Computation that preserves information at every step along the way (and not just by trivially storing the initial data) is called reversible compu- tation

    But in the same paper:“At first sight it may seem that logical reversibility is simply obtained by saving the input in some corner of the machine. We shall, however, label a machine as being log- ically reversible, if and only if all its individual steps are logically reversib...

  7. [15]

    From state 0 or 1 to state S: remove the partition

  8. [16]

    According to Landauer, the thermodynamic irre- versibility of the erasure comes from step 1 that is iden- tified as being free expansion of a single-particle “gas”

    From state S to state 0: perform an isothermal (thermodynamically reversible) compression with a piston. According to Landauer, the thermodynamic irre- versibility of the erasure comes from step 1 that is iden- tified as being free expansion of a single-particle “gas”. 0 1 0 1...

  9. [17]

    reverse step 2 of Landauer erasure)

    From state 0 to state S: use the piston that is al- ready in position to do an isothermal expansion (i.e. reverse step 2 of Landauer erasure)

  10. [18]

    The energy exchanged during the step 3 compensates ex- actly that of step 2, so that the net balance is 0

    From state S to unknown-state: put back the parti- tion, so that the final state is random and unknown. The energy exchanged during the step 3 compensates ex- actly that of step 2, so that the net balance is 0. Step 4 puts the data-bit at a random unknown value exactly as it w...

  11. [19]

    more usual in computing

    From state S to the initial state (0 or 1): use a piston to push the particle into the proper com- partment. This will causeTln 2 of heat dissipation, so that the Lan- dauer procedure to erase the data-bit is actually irre- versible for a known value and only in this case. Thi...

  12. [20]

    Actually thermodynam- ics does not, and whether or not two states differ in thermodynamics depends on the observer and his knowl- edge

    States incompletely defined for thermodynamics The Gibbs paradoxes (§I C 2 and§II D) arise when we mistakenly assume that thermodynamics treats the states of a system as something intrinsic to the sys- tem, such as the total information needed to describe it entirely (if that ...

  13. [21]

    There- fore, according to Newton’s deterministic mechanics, this is not possible because a unique time-varying force can- not cause two trajectories

    Managing two possibilities with a single externally imposed procedure With the Landauer erasure procedure, the externally controlled process to drive the particle in an undeter- mined state (state S) and from there to state 0, is con- ceived as an external force applied to the...

  14. [22]

    The idea that data-bits necessarily store informa- tion. In reality, information is necessarily stored under the form of data-bits but data-bits (even those set to a particular value according to a given acquired piece of information) do not necessarily store infor- mation. Co...

  15. [23]

    The mass of a bit of information and the Brillouin ’s princi- ple

    The idea that Brillouin negentropy principle and Landauer erasure principle are the same (see§IV B) or that the two can be amalgamated:“The mass of a bit of information and the Brillouin ’s princi- ple”[81] in 2014 becomes 6 years later:“We shall first analyze, in the context ...

    2014

  16. [24]

    For 1Tb device the estimated mass change is2.5× 10−25 Kg.”(Vopson [82])

    The idea that information cannot be outdated (then it would no longer be information) so that a data-bit stores information forever, which is closely related to the idea that a piece of information is a self-sufficient entity and that there is no need to specify information ab...

  17. [25]

    The idea that the work required to acquire infor- mation is stored as energy in the data-bit, just as mechanical work exerted on a body can be stored within it as potential energy, but actually under the form of rest mass [92, 93]. In reality, at constant temperature, when a s...

  18. [26]

    Descartes,Meditations on First Philosophy, edited by M

    R. Descartes,Meditations on First Philosophy, edited by M. Moriarty, Oxford World’s Classics Ser. (Oxford Uni- versity Press USA - OSO, Oxford, 2008)

    2008

  19. [27]

    Carter,Descartes’ medical philosophy : the organic solution to the mind-body problem(The Johns Hopkins University, 1931)

    R. Carter,Descartes’ medical philosophy : the organic solution to the mind-body problem(The Johns Hopkins University, 1931)

    1931

  20. [28]

    Mach,The Science of Mechanics(The Open Court Publishing Company, 1919)

    E. Mach,The Science of Mechanics(The Open Court Publishing Company, 1919)

    1919

  21. [29]

    Duhem,The Aim and Structure of Physical Theory (Princeton University Press, 2021)

    P. Duhem,The Aim and Structure of Physical Theory (Princeton University Press, 2021)

    2021

  22. [30]

    Einstein, On the method of theoretical physics, Phi- losophy of Science1, 163 (1934)

    A. Einstein, On the method of theoretical physics, Phi- losophy of Science1, 163 (1934)

    1934

  23. [31]

    Einstein, B

    A. Einstein, B. Podolsky, and N. Rosen, Can quantum- mechanical description of physical reality be considered complete?, Physical Review47, 777 (1935)

    1935

  24. [32]

    J. C. Maxwell,Theory of heat, 3rd ed. (Longmans, Green and Co., London, 1872)

  25. [33]

    Planck,Treatise of thermodynamics(Longmans, Green and Co., 1903)

    M. Planck,Treatise of thermodynamics(Longmans, Green and Co., 1903)

    1903

  26. [34]

    J. C. Maxwell, Diffusion, Encyclopedia Britannica, re- produced in Scientific papers2, 625 (1878)

  27. [35]

    Joule, On the mechanical equivalent of heat, Philo- sophical Transactions of the Royal Society of London 140, 61 (1850)

    J. Joule, On the mechanical equivalent of heat, Philo- sophical Transactions of the Royal Society of London 140, 61 (1850)

  28. [36]

    R. P. Feynman, R. B. Leighton, and M. Sands,The Feyn- man lectures on physics(Addison-Wesley, Reading, MA,

  29. [37]

    Hecht, Understanding energy as a subtle concept: A model for teaching and learning energy, American Jour- nal of Physics87, 495 (2019)

    E. Hecht, Understanding energy as a subtle concept: A model for teaching and learning energy, American Jour- nal of Physics87, 495 (2019)

    2019

  30. [38]

    Clausius,The mechanical theory of heat(Macmillan & Co, London, UK, 1879)

    R. Clausius,The mechanical theory of heat(Macmillan & Co, London, UK, 1879)

  31. [39]

    E. T. Jaynes, The Gibbs paradox, inMaximum Entropy and Bayesian Methods(Springer Netherlands, 1992) pp. 1–21

    1992

  32. [40]

    W. V. Quine,The ways of paradox, and other essays (Harvard University Press, Cambridge, Massachusetts, 1976)

    1976

  33. [41]

    J. W. Gibbs,On the equilibrium of heterogeneous sub- stances : first [-second] part(Connecticut academy of arts and sciences, 1874)

  34. [42]

    Lairez, Thermostatistics, information, subjectivity: Why is this association so disturbing?, Mathematics12, 1498 (2024)

    D. Lairez, Thermostatistics, information, subjectivity: Why is this association so disturbing?, Mathematics12, 1498 (2024)

    2024

  35. [43]

    van Kampen, The Gibbs paradox, inEssays in Theo- retical Physics(Elsevier, 1984) pp

    N. van Kampen, The Gibbs paradox, inEssays in Theo- retical Physics(Elsevier, 1984) pp. 303–312

    1984

  36. [44]

    Szilard, On the decrease of entropy in a thermody- namic system by the intervention of intelligent beings, Behavioral Science9, 301 (1964)

    L. Szilard, On the decrease of entropy in a thermody- namic system by the intervention of intelligent beings, Behavioral Science9, 301 (1964)

    1964

  37. [45]

    Darrigol, Boltzmann’s reply to the Loschmidt para- dox: a commented translation, The European Physical Journal H46, 10.1140/epjh/s13129-021-00029-2 (2021)

    O. Darrigol, Boltzmann’s reply to the Loschmidt para- dox: a commented translation, The European Physical Journal H46, 10.1140/epjh/s13129-021-00029-2 (2021)

    2021 doi

  38. [46]

    C. H. Bennett, Demons, engines and the second law, Sci- entific American257, 108 (1987)

    1987

  39. [47]

    R. L. Liboff, Maxwell’s demon and the second law of thermodynamics, Foundations of Physics Letters10, 89 (1997)

    1997

  40. [48]

    H. S. Leff, Maxwell’s demon and the second law, inAIP Conference Proceedings, Vol. 643 (AIP, 2002) pp. 408– 419

    2002

  41. [49]

    T. D. Kieu, The second law, Maxwell’s demon, and work derivable from quantum heat engines, Physical Review Letters93, 140403 (2004)

    2004

  42. [50]

    Radhakrishnamurty, Maxwell’s demon and the second law of thermodynamics, Resonance15, 548 (2010)

    P. Radhakrishnamurty, Maxwell’s demon and the second law of thermodynamics, Resonance15, 548 (2010)

    2010

  43. [51]

    Ciliberto, Landauer’s bound and Maxwell’s demon, in Information Theory(Springer International Publishing,

    S. Ciliberto, Landauer’s bound and Maxwell’s demon, in Information Theory(Springer International Publishing,

  44. [52]

    P. W. Fontana, Hidden dissipation and irreversibility in Maxwell’s demon, Entropy24, 93 (2022)

    2022

  45. [53]

    Gibbs,Elementary principles in statistical mechanics (Charles Scribner’s sons, 1902)

    J. Gibbs,Elementary principles in statistical mechanics (Charles Scribner’s sons, 1902)

    1902

  46. [54]

    Balian,From microphysics to macrophysics(Springer Berlin Heidelberg, 1991)

    R. Balian,From microphysics to macrophysics(Springer Berlin Heidelberg, 1991)

    1991

  47. [55]

    Dubs, The principle of insufficient reason, Philosophy of Science9, 123 (1942)

    H. Dubs, The principle of insufficient reason, Philosophy of Science9, 123 (1942)

    1942

  48. [56]

    Keynes,A treatise on probability(Macmillian, 1921)

    J. Keynes,A treatise on probability(Macmillian, 1921)

    1921

  49. [57]

    method of least squares,

    R. Ellis, Remarks on an alleged proof of the “method of least squares,” contained in a late number of the ed- inburgh review, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science37, 321 (1850)

  50. [58]

    Lairez, A short derivation of Boltzmann distribution and Gibbs entropy formula from the fundamental postu- 22 late, arXiv (2022), 2211.02455v3

    D. Lairez, A short derivation of Boltzmann distribution and Gibbs entropy formula from the fundamental postu- 22 late, arXiv (2022), 2211.02455v3

    2022 arXiv

  51. [59]

    C. L. Tien and J. Lienhard,Statistical thermodynamics (Hemisphere Pub. Corp., 1979)

    1979

  52. [60]

    Sekerka,Thermal Physics(Elsevier, 2015)

    R. Sekerka,Thermal Physics(Elsevier, 2015)

    2015

  53. [61]

    Boltzmann,Lectures on gas theory(Dover ed., New York, NY, USA, 1964)

    L. Boltzmann,Lectures on gas theory(Dover ed., New York, NY, USA, 1964)

    1964

  54. [62]

    J. C. Maxwell, On the dynamical theory of gases, Philo- sophical Transactions of the Royal Society of London 157, 49 (1867)

  55. [63]

    Cercignani,The Boltzmann Equation and Its Applica- tions(Springer New York, 1988)

    C. Cercignani,The Boltzmann Equation and Its Applica- tions(Springer New York, 1988)

    1988

  56. [64]

    Villani, H-theorem and beyond: Boltzmann’s entropy in today’s mathematics, inBoltzmann ’s Legacy(EMS Press, 2008) pp

    C. Villani, H-theorem and beyond: Boltzmann’s entropy in today’s mathematics, inBoltzmann ’s Legacy(EMS Press, 2008) pp. 129–143

    2008

  57. [65]

    Weaver, In praise of Clausius entropy: Reassessing the foundations of Boltzmannian statistical mechanics, Foundations of Physics51, 10.1007/s10701-021-00437-w (2021)

    C. Weaver, In praise of Clausius entropy: Reassessing the foundations of Boltzmannian statistical mechanics, Foundations of Physics51, 10.1007/s10701-021-00437-w (2021)

    2021 doi

  58. [66]

    C. Weaver, Poincar´ e, Poincar´ e recurrence and the H- theorem: A continued reassessment of Boltzmannian statistical mechanics, International Journal of Modern Physics B36, 10.1142/s0217979222300055 (2022)

    2022 doi

  59. [67]

    Villani, Chap

    C. Villani, Chap. 2 - a review of mathematical topics in collisional kinetic theory, inHandbook of Mathemat- ical Fluid Dynamics, Handbook of Mathematical Fluid Dynamics, Vol. 1, edited by S. Friedlander and D. Serre (North-Holland, 2002) pp. 71–74

    2002

  60. [68]

    Uffink, Compendium of the foundations of classical statistical physics, inPhilosophy of Physics, Handbook of the Philosophy of Science, edited by J

    J. Uffink, Compendium of the foundations of classical statistical physics, inPhilosophy of Physics, Handbook of the Philosophy of Science, edited by J. Butterfield and J. Earman (North-Holland, Amsterdam, 2007) pp. 923– 1074

    2007

  61. [69]

    H. B. Callen,Thermodynamics and an introduction to thermostatistics, 2nd ed. (J. Wiley & sons, 1985)

    1985

  62. [70]

    Villani, (Ir)reversibility and entropy, inTime (Springer Basel, 2012) pp

    C. Villani, (Ir)reversibility and entropy, inTime (Springer Basel, 2012) pp. 19–79

    2012

  63. [71]

    J. R. Ray, Correct Boltzmann counting, European Jour- nal of Physics5, 219 (1984)

    1984

  64. [72]

    Huang,Statistical Mechanics, 2nd ed

    K. Huang,Statistical Mechanics, 2nd ed. (J. Wiley & sons, 1991)

    1991

  65. [73]

    J. F. Nagle, Regarding the entropy of distinguishable par- ticles, Journal of Statistical Physics117, 1047 (2004)

    2004

  66. [74]

    Cheng, Thermodynamics of the system of distin- guishable particles, Entropy11, 326 (2009)

    C.-H. Cheng, Thermodynamics of the system of distin- guishable particles, Entropy11, 326 (2009)

    2009

  67. [75]

    M. A. M. Versteegh and D. Dieks, The Gibbs paradox and the distinguishability of identical particles, American Journal of Physics79, 741 (2011)

    2011

  68. [76]

    Frenkel, Why colloidal systems can be described by statistical mechanics: some not very original comments on the Gibbs paradox, Molecular Physics112, 2325 (2014)

    D. Frenkel, Why colloidal systems can be described by statistical mechanics: some not very original comments on the Gibbs paradox, Molecular Physics112, 2325 (2014)

    2014

  69. [77]

    Dieks, The Gibbs paradox and particle individuality, Entropy20, 466 (2018)

    D. Dieks, The Gibbs paradox and particle individuality, Entropy20, 466 (2018)

    2018

  70. [78]

    Saunders, The Gibbs paradox, Entropy20, 552 (2018)

    S. Saunders, The Gibbs paradox, Entropy20, 552 (2018)

    2018

  71. [79]

    van Lith, The Gibbs paradox: lessons from thermody- namics, Entropy20, 328 (2018)

    J. van Lith, The Gibbs paradox: lessons from thermody- namics, Entropy20, 328 (2018)

    2018

  72. [80]

    Lairez, Plea for the use of the exact Stirling formula in statistical mechanics, SciPost Physics Lecture Notes 10.21468/scipostphyslectnotes.76 (2023)

    D. Lairez, Plea for the use of the exact Stirling formula in statistical mechanics, SciPost Physics Lecture Notes 10.21468/scipostphyslectnotes.76 (2023)

    2023 doi

  73. [81]

    Kobayashi, J

    A. Kobayashi, J. Park, J. Min´ e-Hattab, and F. G. Fern´ andez, A guide for single particle tracking: from sample preparation and image acquisition to the analysis of individual trajectories (2025)

    2025

  74. [82]

    J. C. Crocker and B. D. Hoffman, Multiple-particle track- ing and two-point microrheology in cells, inCell Mechan- ics(Elsevier, 2007) pp. 141–178

    2007

  75. [83]

    S. C. Pinto, N. A. Vickers, F. Sharifi, and S. B. Anders- son, Tracking multiple diffusing particles using informa- tion optimal control, in2021 American Control Confer- ence (ACC)(IEEE, 2021) pp. 4033–4038

    2021

  76. [84]

    X. Xu, J. Wei, and S. Sang, Deep learning-based multiple particle tracking in complex system, AIP Advances14, 10.1063/5.0186670 (2024)

    2024 doi

  77. [85]

    Peters, Demonstration and resolution of the Gibbs paradox of the first kind, European Journal of Physics 35, 015023 (2013)

    H. Peters, Demonstration and resolution of the Gibbs paradox of the first kind, European Journal of Physics 35, 015023 (2013)

    2013

  78. [86]

    C. E. Shannon, A mathematical theory of communica- tion, The Bell System Technical Journal27, 379 (1948)

    1948

  79. [87]

    R. V. L. Hartley, Transmission of information, Bell Sys- tem Technical Journal7, 535 (1928)

    1928

  80. [88]

    E. T. Jaynes, Information theory and statistical mechan- ics, Phys. Rev.106, 620 (1957)

    1957

  81. [89]

    Shore and R

    J. Shore and R. Johnson, Axiomatic derivation of the principle of maximum entropy and the principle of min- imum cross-entropy, IEEE Transactions on Information Theory26, 26 (1980)

    1980

  82. [90]

    E. T. Jaynes, The well-posed problem, Foundations of Physics3, 477 (1973)

    1973

  83. [91]

    Brillouin, The negentropy principle of information, Journal of Applied Physics24, 1152 (1953)

    L. Brillouin, The negentropy principle of information, Journal of Applied Physics24, 1152 (1953)

    1953

  84. [92]

    Brillouin,Science and Information Theory(Dover Publications, Mineola, N.Y., 1956)

    L. Brillouin,Science and Information Theory(Dover Publications, Mineola, N.Y., 1956)

    1956

  85. [93]

    Ciliberto, Landauer’s bound and maxwell’s demon, S´ eminaire Poincar´ eL’Information, XXIII, 79 (2018)

    S. Ciliberto, Landauer’s bound and maxwell’s demon, S´ eminaire Poincar´ eL’Information, XXIII, 79 (2018)

    2018

  86. [94]

    Penrose, Foundations of statistical mechanics, Reports on Progress in Physics42, 1937 (1979)

    O. Penrose, Foundations of statistical mechanics, Reports on Progress in Physics42, 1937 (1979)

    1979

  87. [95]

    Denbigh and J

    K. Denbigh and J. Denbigh,Entropy in Relation to In- complete Knowledge(Cambridge University Press, 1985)

    1985

  88. [96]

    D. A. Lavis, Frontiers in fundamental physics, inFron- tiers in Fundamental Physics, Vol. vol 3, edited by B. G. Sidarth (Universities Press, India,, 2007) Chap. Equilib- rium and (Ir)reversibility in Classical Statistical Mechan- ics

    2007

  89. [97]

    Landauer, Information is physical, Physics Today44, 23 (1991)

    R. Landauer, Information is physical, Physics Today44, 23 (1991)

    1991

  90. [98]

    Landauer, Irreversibility and heat generation in the computing process, IBM Journal of Research and Devel- opment5, 183 (1961)

    R. Landauer, Irreversibility and heat generation in the computing process, IBM Journal of Research and Devel- opment5, 183 (1961)

    1961

  91. [99]

    Landauer, The physical nature of information, Physics Letters A217, 188 (1996)

    R. Landauer, The physical nature of information, Physics Letters A217, 188 (1996)

    1996

  92. [100]

    C. H. Bennett, The thermodynamics of computation - a review, International Journal of Theoretical Physics21, 905 (1982)

    1982

  93. [101]

    C. H. Bennett, Notes on Landauer's principle, reversible computation, and Maxwell's demon, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics34, 501 (2003)

    2003

  94. [102]

    Herrera, Landauer principle and general relativity, En- tropy22, 340 (2020)

    L. Herrera, Landauer principle and general relativity, En- tropy22, 340 (2020)

    2020

  95. [103]

    Lutz and S

    E. Lutz and S. Ciliberto, Information: from Maxwell’s demon to Landauer’s eraser, Physics Today68, 30 (2015)

    2015

  96. [104]

    Bormashenko, The Landauer principle: Re- formulation of the second thermodynamics law or a step to great unification?, Entropy21, 918 (2019)

    E. Bormashenko, The Landauer principle: Re- formulation of the second thermodynamics law or a step to great unification?, Entropy21, 918 (2019)

    2019

  97. [105]

    Witkowski, S

    C. Witkowski, S. Brown, and K. Truong, On the precise link between energy and information, Entropy26, 203 (2024). 23

    2024

  98. [106]

    Herrera, The mass of a bit of information and the Brillouin’s principle, Fluctuation and Noise Letters13, 1450002 (2014)

    L. Herrera, The mass of a bit of information and the Brillouin’s principle, Fluctuation and Noise Letters13, 1450002 (2014)

    2014

  99. [107]

    M. M. Vopson, The mass-energy-information equivalence principle, AIP Advances9, 095206 (2019)

    2019

  100. [108]

    M. M. Vopson, The information catastrophe, AIP Ad- vances10, 10.1063/5.0019941 (2020)

    2020 doi

  101. [109]

    E. Dˇ zaferovi´ c-Maˇ si´ c, Missing information in the universe as a dark matter candidate based on the mass-energy- information equivalence principle, Journal of Physics: Conference Series1814, 012006 (2021)

    2021

  102. [110]

    M. M. Vopson, Experimental protocol for testing the mass-energy-information equivalence principle, AIP Ad- vances12, 035311 (2022)

    2022

  103. [111]

    Ciliberto and E

    S. Ciliberto and E. Lutz, The physics of information: from Maxwell to Landauer, inEnergy Limits in Com- putation(Springer International Publishing, 2018) pp. 155–175

    2018

  104. [112]

    Lairez, The fundamental difference between boolean logic and thermodynamic irreversibilities, or, why Lan- dauer’s result cannot be a physical principle, Symmetry 16, 1594 (2024)

    D. Lairez, The fundamental difference between boolean logic and thermodynamic irreversibilities, or, why Lan- dauer’s result cannot be a physical principle, Symmetry 16, 1594 (2024)

    2024

  105. [113]

    M. B. Plenio and V. Vitelli, The physics of forget- ting: Landauer’s erasure principle and information the- ory, Contemporary Physics42, 25 (2001)

    2001

  106. [114]

    O. Maroney, The (absence of a) relationship between thermodynamic and logical reversibility, Studies in His- tory and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics36, 355 (2005)

    2005

  107. [115]

    Lairez, Thermodynamical versus logical irreversibility: A concrete objection to Landauer’s principle, Entropy 25, 1155 (2023)

    D. Lairez, Thermodynamical versus logical irreversibility: A concrete objection to Landauer’s principle, Entropy 25, 1155 (2023)

    2023

  108. [116]

    Lairez, On the supposed mass of entropy and that of information, Entropy26, 337 (2024)

    D. Lairez, On the supposed mass of entropy and that of information, Entropy26, 337 (2024)

    2024

  109. [117]

    Brillouin, The actual mass of potential energy, a cor- rection to classical relativity, PNAS53, 475 (1965)

    L. Brillouin, The actual mass of potential energy, a cor- rection to classical relativity, PNAS53, 475 (1965)

    1965

  110. [118]

    Brillouin, The actual mass of potential energy II, PNAS53, 1280 (1965)

    L. Brillouin, The actual mass of potential energy II, PNAS53, 1280 (1965)

    1965

  111. [119]

    Rosenblum and F

    B. Rosenblum and F. Kuttner, Foundations of Physics 32, 1273 (2002)

    2002

  112. [120]

    Feynman, The Feynman lectures on physics vol

    R. Feynman, The Feynman lectures on physics vol. I, chap. 15: The special theory of relativity (1963)

    1963

  113. [121]

    Bini, Observers, observables and measurements in general relativity, inGeneral Relativity, Cosmology and Astrophysics(Springer International Publishing, 2014) pp

    D. Bini, Observers, observables and measurements in general relativity, inGeneral Relativity, Cosmology and Astrophysics(Springer International Publishing, 2014) pp. 67–90

    2014

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