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arxiv: 2510.13145 · v2 · submitted 2025-10-15 · ❄️ cond-mat.soft · cond-mat.stat-mech

Demon's variational principle for informational active matter

Kento Yasuda , Kenta Ishimoto , Shigeyuki Komura This is my paper

Pith reviewed 2026-05-18 07:02 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.stat-mech
keywords informational Onsager-Machlup principleactive matterstochastic thermodynamicsinformation thermodynamicsfeedback controlinformation-driven swimmervariational principlepath entropy
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0 comments X p. Extension

The pith

A variational principle unifies energy, dissipation, and information in feedback-controlled active systems.

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

This paper develops a generalized variational framework that treats information and feedback as contributions on equal footing with energy and dissipation. The approach introduces a conditioned integral to capture path entropy given specific memory states and derives cumulant generating functions for observables in measurement-and-control settings. When applied to a minimal information-driven swimmer, it produces exact expressions for velocity statistics in the single-measurement case and approximate expressions under a Gaussian closure for repeated measurements and steady state. The results remain consistent with stochastic and information thermodynamics. A sympathetic reader would care because the framework supplies a systematic route to predict average motion and fluctuations in microscopic agents that sense and react to their surroundings.

Core claim

We develop the informational Onsager-Machlup principle, a generalized variational framework that unifies energetic, dissipative, and informational contributions within a single formalism. This framework introduces a conditioned Onsager-Machlup integral to quantify path entropy under specified memory states and enables the derivation of cumulant generating functions for arbitrary observables in systems with measurement and feedback. Our formulation is consistent with stochastic thermodynamics and information thermodynamics. Applying this principle to a minimal model of an information-driven swimmer, we obtain analytical expressions for the mean velocity and higher-order cumulants in the单测量案例.

What carries the argument

The informational Onsager-Machlup principle, a variational framework that adds informational contributions to the classical Onsager-Machlup action and uses a conditioned integral to encode memory-state dependence.

If this is right

  • Exact analytical expressions for mean velocity and higher cumulants follow directly for the single-measurement swimmer.
  • Approximate closed-form expressions for velocity statistics emerge for repeated measurements and steady state once the Gaussian closure is imposed.
  • The framework recovers known limits of stochastic thermodynamics and information thermodynamics as special cases.
  • Agreement with direct numerical integration holds except in regimes of extreme drag asymmetry.

Where Pith is reading between the lines

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

  • The same conditioned-integral construction could be used to analyze efficiency bounds in other feedback-regulated active particles.
  • Relaxing the Gaussian assumption would allow direct comparison of non-Gaussian fluctuation statistics in strongly asymmetric drag cases.
  • The variational structure suggests a route to optimize control protocols that minimize total dissipation for a target mean speed.

Load-bearing premise

The Gaussian closure approximation accurately captures the distribution of measured velocities for repeated measurements and in the steady state.

What would settle it

Numerical sampling of swimmer trajectories under extreme drag asymmetry that produces clear deviations from the Gaussian-predicted cumulants would falsify the approximation.

Figures

Figures reproduced from arXiv: 2510.13145 by Kenta Ishimoto, Kento Yasuda, Shigeyuki Komura.

Figure 2
Figure 2. Figure 2: FIG. 2. Schematic flowchart of the informational Onsager [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Schematic illustration of the information swim [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) First cumulant [see Eq. (12)], (b) second cumulant [see Eq. (13)], (c) third cumulant [see Eq. (E4)], and (d) fourth [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. First cumulant [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Cumulant generating function [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

The interplay between information, dissipation, and control is reshaping our understanding of thermodynamics in feedback-regulated systems. We develop the informational Onsager-Machlup principle, a generalized variational framework that unifies energetic, dissipative, and informational contributions within a single formalism. This framework introduces a conditioned Onsager-Machlup integral to quantify path entropy under specified memory states and enables the derivation of cumulant generating functions for arbitrary observables in systems with measurement and feedback. Our formulation is consistent with stochastic thermodynamics and information thermodynamics. Applying this principle to a minimal model of an information-driven swimmer, we obtain analytical expressions for the mean velocity and higher-order cumulants in the single-measurement case. For repeated measurements and the steady state, we derive approximate analytical expressions by using a Gaussian closure for the distribution of measured velocities. Our analytical expression shows good agreement with numerical results, except for cases of extreme drag asymmetry.

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

1 major / 2 minor

Summary. The manuscript develops the informational Onsager-Machlup principle, a generalized variational framework unifying energetic, dissipative, and informational contributions for active matter systems with measurement and feedback. It introduces a conditioned Onsager-Machlup integral to quantify path entropy under specified memory states and derives cumulant generating functions for arbitrary observables. The framework is shown to be consistent with stochastic and information thermodynamics. Applied to a minimal information-driven swimmer model, it yields analytical expressions for mean velocity and higher cumulants in the single-measurement case; for repeated measurements in steady state, approximate closed-form expressions are obtained via a Gaussian closure on the measured-velocity distribution, with reported agreement to numerics except at extreme drag asymmetry.

Significance. If the central construction holds, the work provides a variational unification of information with Onsager-Machlup dynamics that could facilitate analytical treatment of feedback-controlled active systems. The explicit derivation of cumulant generating functions and the numerical validation for the swimmer model are strengths; the consistency with established thermodynamic frameworks adds credibility. The Gaussian-closure results, however, require clearer bounds to realize the claimed generality for arbitrary observables.

major comments (1)
  1. [Repeated measurements and steady-state analysis] In the repeated-measurement steady-state analysis, the Gaussian closure is applied to the distribution of measured velocities to close the cumulant generating function and obtain analytical expressions for the information-driven swimmer. No error bounds, higher-moment comparisons, or Kullback-Leibler divergence to the true distribution are supplied, nor is a regime of validity delineated. This step is load-bearing for the steady-state claims and the reported exception at extreme drag asymmetry suggests the approximation may degrade under moderate feedback strengths.
minor comments (2)
  1. [Framework derivation] The manuscript should explicitly demonstrate how the conditioned Onsager-Machlup integral reduces to the standard Onsager-Machlup functional when information/feedback terms vanish, to strengthen the consistency claim.
  2. Notation for the memory-state conditioning and the path-entropy measure could be clarified with a dedicated table or appendix to aid readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We appreciate the positive assessment of the informational Onsager-Machlup principle, its consistency with thermodynamic frameworks, and the numerical validation for the swimmer model. We address the major comment on the Gaussian closure below.

read point-by-point responses

  1. Referee: [Repeated measurements and steady-state analysis] In the repeated-measurement steady-state analysis, the Gaussian closure is applied to the distribution of measured velocities to close the cumulant generating function and obtain analytical expressions for the information-driven swimmer. No error bounds, higher-moment comparisons, or Kullback-Leibler divergence to the true distribution are supplied, nor is a regime of validity delineated. This step is load-bearing for the steady-state claims and the reported exception at extreme drag asymmetry suggests the approximation may degrade under moderate feedback strengths.

    Authors: We agree that additional quantitative support for the Gaussian closure would strengthen the steady-state results. In the revised manuscript we will add a new paragraph (or short appendix) that compares the first four cumulants obtained from the closure against direct numerical simulations over a range of feedback strengths, including moderate values. We will also report the Kullback-Leibler divergence between the Gaussian approximation and the sampled measured-velocity distribution at representative points and will delineate the regime of validity by identifying a simple criterion (based on the measured skewness or variance) beyond which the approximation degrades. The existing statement that agreement holds except at extreme drag asymmetry will be retained and explicitly linked to this criterion, thereby clarifying the applicability of the analytical expressions without altering the central claims of the work. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained with independent content

full rationale

The paper introduces the informational Onsager-Machlup principle as a new variational framework unifying energetic, dissipative, and informational terms, then derives cumulant generating functions from a conditioned integral. The Gaussian closure is explicitly presented as an approximation for the repeated-measurement steady state, validated by comparison to numerical results rather than by construction or self-citation. No load-bearing step reduces to a fitted input renamed as prediction, self-definitional loop, or uniqueness theorem imported from the authors' prior work. The central claims remain independent of the target results and rest on consistency with stochastic and information thermodynamics plus direct numerical checks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Based solely on abstract; no explicit free parameters identified. The stated consistency with prior thermodynamics is treated as a domain assumption. The conditioned integral is a new construct without independent evidence shown.

axioms (1)
  • domain assumption The formulation is consistent with stochastic thermodynamics and information thermodynamics.
    Explicitly stated in the abstract as a foundational property of the new principle.
invented entities (1)
  • conditioned Onsager-Machlup integral no independent evidence
    purpose: To quantify path entropy under specified memory states in systems with measurement and feedback.
    Introduced as the key new element enabling the variational framework and cumulant derivations.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Covariant Onsager and Onsager-Machlup principles for active and inertial dynamics

    cond-mat.soft 2026-04 unverdicted novelty 7.0

    Covariant Onsager and Onsager-Machlup principles are derived for active matter with inertia, yielding geometrically consistent dynamics and path probabilities that satisfy the detailed fluctuation theorem.

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