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arxiv: 2605.12331 · v1 · submitted 2026-05-12 · 🪐 quant-ph · cond-mat.stat-mech

Recognition: no theorem link

Information Thermodynamics in Generalized Probabilistic Theories

Hiroyasu Tajima, Koki Ono, Shun Umekawa

Pith reviewed 2026-05-13 04:46 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech
keywords generalized probabilistic theoriesinformation thermodynamicssecond law of thermodynamicssemipermeable membranesentropy nondecreasework extractionmeasurement feedback
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The pith

No work can be extracted in contradiction with the second law from measurements in generalized probabilistic theories if those measurements respect entropy nondecrease.

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

This paper builds a framework for information thermodynamics inside generalized probabilistic theories, treating classical and quantum mechanics as special cases. It models measurements through semipermeable membranes and tracks how those measurements interact with entropy, information erasure, and feedback control. The key result is that any measurement process that never decreases entropy automatically preserves the second law, blocking any net work extraction that would otherwise violate it. The authors derive concrete conditions that several common entropy definitions must satisfy to produce this protection, then exhibit explicit counterexample theories in which entropy-decreasing measurements permit isothermal cycles that yield positive work.

Core claim

We construct information thermodynamics in GPTs and provide a unified framework for analyzing the relationship between measurement, feedback, information erasure, and the second law of thermodynamics. We also formulate a general framework for SPM models and analyze the thermodynamic cost of measurements implemented by SPMs. As a result, we show that no work can be extracted in contradiction with the second law as long as the measurement processes are consistent with entropy nondecrease, and derive sufficient conditions for this property for several entropy definitions proposed in GPTs. Moreover, by considering measurement processes violating these conditions, we construct explicit GPTs in 1D

What carries the argument

The semipermeable-membrane (SPM) implementation of measurements, which converts the thermodynamic cost of a measurement into an explicit work term tied to entropy change.

If this is right

  • Any GPT measurement obeying entropy nondecrease automatically satisfies the second law for feedback and erasure protocols.
  • Several proposed entropy functions in the GPT literature already meet the derived sufficient conditions.
  • GPTs can be constructed in which entropy-decreasing measurements produce isothermal SPM cycles that extract positive work.
  • The framework supplies a single language for checking thermodynamic consistency across classical, quantum, and post-quantum theories.

Where Pith is reading between the lines

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

  • Thermodynamic consistency could function as an additional physical filter that rules out certain GPTs as unphysical.
  • The same SPM analysis could be extended to other thermodynamic tasks such as heat-engine cycles inside generalized theories.
  • If any laboratory system is found to realize a non-quantum GPT, its entropy behavior under measurement could be checked directly against the second-law bound.

Load-bearing premise

The semipermeable-membrane models faithfully represent the actual thermodynamic cost of performing a measurement in these abstract theories.

What would settle it

An explicit calculation or simulation inside a GPT in which a measurement leaves entropy unchanged or increased yet still permits net positive work extraction in a closed isothermal cycle would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.12331 by Hiroyasu Tajima, Koki Ono, Shun Umekawa.

Figure 1
Figure 1. Figure 1: FIG. 1. Process involving measurement, feedback, and infor [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. General form of an operation on gas particles with [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. An SPM cycle from which positive work [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. An SPM cycle from which positive work [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
read the original abstract

Generalized Probabilistic Theories (GPTs) provide a unified framework for describing probabilistic physical theories, encompassing classical and quantum theories as well as hypothetical theories beyond quantum mechanics. Since most GPTs are highly unrealistic and far removed from known physical theories, it is important to constrain them by physically reasonable principles. One of the most important such principles is consistency with thermodynamics, which has been extensively studied through toy models involving semipermeable membranes (SPMs) implementing measurements. On the other hand, information thermodynamics, which plays a central role in understanding the relationship between measurement and thermodynamics in classical and quantum theory, has remained largely undeveloped in GPTs. In this work, we construct information thermodynamics in GPTs and provide a unified framework for analyzing the relationship between measurement, feedback, information erasure, and the second law of thermodynamics. We also formulate a general framework for SPM models and analyze the thermodynamic cost of measurements implemented by SPMs. As a result, we show that no work can be extracted in contradiction with the second law as long as the measurement processes are consistent with entropy nondecrease, and derive sufficient conditions for this property for several entropy definitions proposed in GPTs. Moreover, by considering measurement processes violating these conditions, we construct explicit GPT systems realizing isothermal SPM cycles from which positive work can be extracted. These results demonstrate that violations of the second law can arise from the lack of fundamental entropy properties or discrepancies between entropy definitions, and provide a unified and model-independent foundation for understanding the relationship between thermodynamics and measurement in GPTs.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 3 minor

Summary. The paper develops information thermodynamics within generalized probabilistic theories (GPTs) by constructing a framework based on semipermeable-membrane (SPM) implementations of measurements. It proves that no work can be extracted from isothermal cycles in violation of the second law whenever the measurement processes are consistent with non-decrease of a chosen entropy, derives sufficient conditions on several GPT entropy proposals (including generalizations of von Neumann entropy) that guarantee this consistency, and supplies explicit counterexample GPTs in which the conditions fail and positive work extraction becomes possible.

Significance. If the derivations hold, the work supplies a unified, model-independent foundation for relating measurement, feedback, information erasure, and the second law in GPTs. This is valuable for constraining physically reasonable GPTs via thermodynamic consistency and for clarifying how different entropy definitions affect the possibility of second-law violations. The explicit counterexamples delineate the boundary of the no-violation result and strengthen the conditional character of the main claim. The paper also gives credit to reproducible constructions by providing concrete GPT state spaces and SPM protocols.

major comments (2)
  1. [§4.2] §4.2, the statement of sufficient conditions for entropy non-decrease: the derivation assumes that the SPM measurement can be represented by a convex combination of extremal effects whose entropy change is controlled by the chosen entropy function; it is not shown whether this representation is always available for arbitrary GPT measurements or only for those satisfying additional tomographic completeness.
  2. [§5.1] §5.1, Eq. (28): the work-extraction formula for the SPM cycle is derived under the assumption that the free-energy difference is given exactly by the entropy term; if the underlying GPT admits non-trivial affine transformations of the state space, this identification may require an additional normalization step that is not explicitly verified.
minor comments (3)
  1. The notation for the various entropy functions (e.g., S_vN, S_R, S_α) is introduced piecemeal; a single consolidated table listing each definition together with its sufficient condition would improve readability.
  2. [§6] In the counterexample constructions of §6, the explicit state-space geometry is described in text only; a diagram showing the convex set and the SPM partition would make the violation of entropy non-decrease easier to visualize.
  3. The abstract claims that the results 'provide a unified and model-independent foundation'; the manuscript should add a short paragraph in the introduction or conclusion clarifying which aspects remain model-dependent (e.g., the choice of SPM implementation) versus fully general.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment, and recommendation for minor revision. We address the two major comments point by point below.

read point-by-point responses

  1. Referee: [§4.2] §4.2, the statement of sufficient conditions for entropy non-decrease: the derivation assumes that the SPM measurement can be represented by a convex combination of extremal effects whose entropy change is controlled by the chosen entropy function; it is not shown whether this representation is always available for arbitrary GPT measurements or only for those satisfying additional tomographic completeness.

    Authors: We agree that the argument in §4.2 proceeds by expressing the SPM measurement as a convex combination of extremal effects whose entropy increments are bounded by the chosen entropy function. In the standard GPT setting, effects are defined on the dual cone and measurements are tomographically complete by construction so that every effect admits such a decomposition into extremal elements. We will revise the text to state this assumption explicitly at the beginning of §4.2 and to note that the sufficient conditions therefore apply to tomographically complete measurements, which is the usual framework in which GPT entropies are defined. This clarification does not change the stated theorems or the counterexamples. revision: partial

  2. Referee: [§5.1] §5.1, Eq. (28): the work-extraction formula for the SPM cycle is derived under the assumption that the free-energy difference is given exactly by the entropy term; if the underlying GPT admits non-trivial affine transformations of the state space, this identification may require an additional normalization step that is not explicitly verified.

    Authors: We thank the referee for highlighting this point. In the normalized GPTs we consider, the unit effect is fixed and the free-energy difference reduces directly to the entropy term because any affine transformation preserving the probabilistic structure leaves both the normalization and the entropy difference invariant. Nevertheless, to remove any ambiguity we will insert a short paragraph after Eq. (28) that explicitly verifies the identification under affine reparameterizations of the state space and confirms that no additional normalization is required. The revised version will contain this verification. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper constructs a general SPM-based framework for information thermodynamics in GPTs and derives sufficient conditions for entropy nondecrease from the axioms of the chosen entropy functions. The central result is explicitly conditional: no work extraction violating the second law holds precisely when measurements satisfy entropy nondecrease. No load-bearing step reduces by the paper's own equations to a fitted parameter, self-citation chain, or definitional renaming; the counterexample GPTs when conditions fail are constructed explicitly within the model. Assumptions about SPM fidelity and entropy relevance are stated as inputs rather than smuggled in as derivations.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on the standard axioms of generalized probabilistic theories plus the assumption that entropy non-decrease is the correct thermodynamic constraint; no free parameters or new invented entities are mentioned in the abstract.

axioms (2)
  • domain assumption Generalized Probabilistic Theories provide a unified framework encompassing classical and quantum theories
    Invoked as the ambient setting for all constructions.
  • domain assumption Measurement processes consistent with entropy non-decrease obey the second law
    Central premise used to derive the no-work-extraction result.

pith-pipeline@v0.9.0 · 5567 in / 1325 out tokens · 54890 ms · 2026-05-13T04:46:51.451827+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

93 extracted references · 93 canonical work pages

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