pith. sign in

arxiv: 2604.11953 · v1 · submitted 2026-04-13 · ❄️ cond-mat.stat-mech · cond-mat.soft

Perspective: Measuring physical entropy out of equilibrium

Haim Diamant , Gil Ariel This is my paper

Pith reviewed 2026-05-10 16:18 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.soft
keywords nonequilibrium entropyphysical systemsinformation theorysteady statesjammed packingsswarming bacteriaentropy measurementabsorbing states
0
0 comments X

The pith

Approaches have been developed to measure entropy in physical nonequilibrium steady states by connecting it to information despite inaccessible full microscopic distributions.

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

This perspective reviews methods developed to quantify entropy in nonequilibrium physical systems such as jammed particle packings and swarming bacteria. These methods rely on the relation between entropy and information to work with the partial data typically available in experiments. A sympathetic reader would care because entropy indicates disorder, structure, and the potential for change, so measuring it out of equilibrium would allow tracking dynamic processes in materials and living matter that never settle into balance. The paper notes that applying these ideas to real physical systems differs from general statistical entropy estimation because of physical constraints and measurable observables. The reviewed applications show the methods can locate structures and transitions in diverse cases.

Core claim

Entropy is well-defined for nonequilibrium steady or absorbing states through its relation to information. Applying this relation to physical systems poses an ongoing challenge because it requires knowledge of microscopic high-dimensional continuous distributions that is generally unattainable. A set of new approaches for the measurement of entropy in nonequilibrium steady or absorbing states have been developed and successfully applied to identify dynamic structures and transitions in diverse systems, ranging from jammed packings to swarming bacteria.

What carries the argument

Information-based entropy estimation methods adapted to physical observables and constraints in nonequilibrium steady or absorbing states.

If this is right

  • Entropy measurements can identify dynamic structures within jammed packings.
  • The same measurements can detect transitions in systems of swarming bacteria.
  • The approaches extend characterization of states beyond what equilibrium thermodynamics provides.
  • Further applications become feasible across other nonequilibrium physical and biological systems.

Where Pith is reading between the lines

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

  • These entropy measures could inform design of active materials that maintain desired levels of disorder.
  • Links may appear between physical entropy estimates and information flow in biological groups.
  • Combining the methods with simulations could predict transitions before they are observed experimentally.

Load-bearing premise

That the entropy-information relation can be applied usefully to physical systems even without access to complete high-dimensional microscopic distributions.

What would settle it

A controlled nonequilibrium experiment, such as on a bacterial swarm or jammed packing, in which entropy values from the new methods show no correlation with independently observed structural changes or transitions.

Figures

Figures reproduced from arXiv: 2604.11953 by Gil Ariel, Haim Diamant.

Figure 1
Figure 1. Figure 1: FIG. 1. Measuring entropy in and out of equilibrium. (a) Entropy change with temperature [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Demonstration of the difficulty in estimating the entropy of systems with continuous [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
read the original abstract

Entropy is one of the key thermodynamic variables reflecting changes in the state of matter. Unlike other thermodynamic variables, it is well-defined also for nonequilibrium steady states through its relation to information. Applying this relation to physical systems is an ongoing challenge, as it requires knowledge of microscopic high-dimensional continuous distributions which is generally unattainable. A set of new approaches for the measurement of entropy in nonequilibrium steady or absorbing states have been developed and successfully applied to identify dynamic structures and transitions in diverse systems, ranging from jammed packings to swarming bacteria. We briefly review these approaches, emphasizing why applications to physical systems, including those out of equilibrium, is substantially different from the general statistical challenge of entropy estimation and inference. We point at promising current and future directions.

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

0 major / 3 minor

Summary. The manuscript is a perspective article that reviews recent approaches developed for measuring physical entropy in nonequilibrium steady states and absorbing states. It identifies the core challenge of unattainable high-dimensional microscopic distributions, describes successful applications of these methods to identify dynamic structures and transitions in systems such as jammed packings and swarming bacteria, and emphasizes distinctions from generic statistical entropy estimation and inference. The text points to promising future directions without presenting new derivations or data.

Significance. As a perspective synthesizing methods for entropy measurement in physical nonequilibrium systems, the work could usefully guide researchers in statistical mechanics by clarifying why physical applications differ from abstract estimation problems and by cataloging concrete successes across diverse systems. Its value lies in the review's breadth and the explicit framing of the information-entropy relation for out-of-equilibrium cases, provided the cited applications are accurately represented.

minor comments (3)
  1. [Abstract] The abstract states that the approaches 'have been developed and successfully applied' but provides no quantitative indicators of success (e.g., error bars, comparison to known limits, or specific observables extracted). Adding one concrete example with a numerical outcome in the main text would make the central claim more tangible without altering the review format.
  2. The distinction drawn between physical entropy measurement and 'the general statistical challenge of entropy estimation' is asserted but not illustrated with a side-by-side comparison of requirements (dimensionality, sampling constraints, or observables). A short table or paragraph contrasting the two would clarify the paper's key pedagogical point.
  3. Several systems are listed (jammed packings, swarming bacteria) but the review does not indicate whether the cited works used the same entropy estimator or different variants; a brief taxonomy of the reviewed methods would help readers assess transferability.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of the manuscript, recognition of its potential utility in guiding researchers, and recommendation for minor revision. The referee's description accurately reflects the scope and intent of this perspective article.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

This is a perspective/review article summarizing external literature on entropy measurement methods in nonequilibrium systems. No new derivations, equations, fitted parameters, or predictions are presented that could reduce to the paper's own inputs by construction. The abstract and structure emphasize review of diverse applications (jammed packings to swarming bacteria) and distinctions from generic statistical estimation, with claims grounded in cited external work rather than self-referential steps. No self-citation load-bearing, ansatz smuggling, or renaming of known results occurs in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central premise rests on the information-theoretic definition of entropy being applicable to nonequilibrium steady states, which is a standard domain assumption rather than a new postulate.

axioms (1)
  • domain assumption Entropy is well-defined for nonequilibrium steady states through its relation to information.
    Explicitly stated in the abstract as the foundation for the reviewed measurement approaches.

pith-pipeline@v0.9.0 · 5416 in / 1105 out tokens · 58188 ms · 2026-05-10T16:18:12.332229+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

45 extracted references · 45 canonical work pages

  1. [1]

    Belkahla, K

    A. Belkahla, K. Cherif, H. Belmabrouk, J.·Bajahzar, A. Dhahri, and E. K. Hlil, Appl. Phys. A125, 443 (2019)

    work page 2019

  2. [2]

    Stochastic thermodynamics, fluctuation theorems, and molecular machines

    U. Seifert, Rep. Prog. Phys.75, 126001 (2012), arXiv:1205.4176

    work page Pith review arXiv 2012

  3. [3]

    D. S. Seara, B. B. Machta, and M. P. Murrell, Nat. Commun.12, 392 (2021)

    work page 2021

  4. [4]

    Peliti and S

    L. Peliti and S. Pigolotti,Stochastic Thermodynamics: An Introduction(Princeton University Press, 2021)

    work page 2021

  5. [5]

    Sorkin, H

    B. Sorkin, H. Diamant, G. Ariel, and T. Markovich, Phys. Rev. Lett.133, 028201 (2024)

    work page 2024

  6. [6]

    Vicsek, A

    T. Vicsek, A. Czir´ ok, E. Ben-Jacob, I. Cohen, and O. Shochet, Phys. Rev. Lett.75, 1226 (1995)

    work page 1995

  7. [7]

    Sorkin, A

    B. Sorkin, A. Be’er, H. Diamant, and G. Ariel, Soft Matter19, 5118 (2023)

    work page 2023

  8. [8]

    F. M. Willems, Y. M. Shtarkov, and T. J. Tjalkens, IEEE transactions on information theory 41, 653 (2002)

    work page 2002

  9. [9]

    Martiniani, P

    S. Martiniani, P. M. Chaikin, and D. Levine, Phys. Rev. X9, 011031 (2019)

    work page 2019

  10. [10]

    Avinery, M

    R. Avinery, M. Kornreich, and R. Beck, Phys. Rev. Lett.123, 178102 (2019)

    work page 2019

  11. [11]

    Cavagna, P

    A. Cavagna, P. M. Chaikin, D. Levine, S. Martiniani, A. Puglisi, and M. Viale, Phys. Rev. E 103, 062141 (2021)

    work page 2021

  12. [12]

    Martiniani, Y

    S. Martiniani, Y. Lemberg, P. M. Chaikin, and D. Levine, Phys. Rev. Lett.125, 170601 (2020)

    work page 2020

  13. [13]

    M. Zu, A. Bupathy, D. Frenkel, and S. Sastry, J. Stat. Mech. , 023204 (2020)

    work page 2020

  14. [14]

    Ariel and H

    G. Ariel and H. Diamant, Phys. Rev. E102, 022110 (2020)

    work page 2020

  15. [15]

    H. S. Green, Proc. R. Soc. London A189, 103 (1947). 11

    work page 1947

  16. [16]

    B. B. Laird and A. D. J. Haymet, Phys. Rev. A45, 5680 (1992)

    work page 1992

  17. [17]

    Sorkin, J

    B. Sorkin, J. Ricouvier, H. Diamant, and G. Ariel, Phys. Rev. E107, 014138 (2023)

    work page 2023

  18. [18]

    M. I. Belghazi, A. Barber, S. Drber, S. Ozair, J. Pineau, A. Courville, and Y. Bengio, in Proceedings of the 35th International Conference on Machine Learning, Vol. 80, edited by J. Dy and A. Krause (PMLR, 2018) pp. 531–540

    work page 2018

  19. [19]

    M. D. Donsker and S. S. Varadhan, Commun. Pure Appl. Math.28, 1 (1975)

    work page 1975

  20. [20]

    A. Nir, E. Sela, R. Beck, and Y. Bar-Sinai, Proc. Natl. Acad. Sci. USA117, 30234 (2020)

    work page 2020

  21. [21]

    S. D. Gelman and G. Cohen, arXiv preprint arXiv:2405.04877 (2024)

    work page arXiv 2024

  22. [22]

    Sorkin, H

    B. Sorkin, H. Diamant, and G. Ariel, Phys. Rev. Lett.131, 147101 (2023)

    work page 2023

  23. [23]

    Rosenfeld, Phys

    Y. Rosenfeld, Phys. Rev. A15, 2545 (1977)

    work page 1977

  24. [24]

    J. C. Dyre, J. Chem. Phys.149, 210901 (2018)

    work page 2018

  25. [25]

    von Neumann,Mathematical Foundations of Quantum Mechanics(Princeton University Press, 1955)

    J. von Neumann,Mathematical Foundations of Quantum Mechanics(Princeton University Press, 1955)

    work page 1955

  26. [26]

    M. M. Wilde, arXiv preprint arXiv:1106.1445v8 (2019)

    work page arXiv 2019

  27. [27]

    A. C. Barato and U. Seifert, Phys. Rev. Lett.114, 158101 (2015)

    work page 2015

  28. [28]

    T. R. Gingrich, J. M. Horowitz, N. Perunov, and J. L. England, Phys. Rev. Lett.116, 120601 (2016)

    work page 2016

  29. [29]

    J. Li, J. M. Horowitz, T. R. Gingrich, and N. Fakhri, Nat. Commun.10, 1666 (2019)

    work page 2019

  30. [30]

    S. K. Manikandan, D. Gupta, and S. Krishnamurthy, Phys. Rev. Lett.124, 120603 (2020)

    work page 2020

  31. [31]

    D. J. Skinner and J. Dunkel, Phys. Rev. Lett.127, 198101 (2021)

    work page 2021

  32. [32]

    Van der Meer, B

    J. Van der Meer, B. Ertel, and U. Seifert, Phys. Rev. X12, 031025 (2022)

    work page 2022

  33. [33]

    P. E. Harunari, A. Dutta, M. Polettini, and ´E. Rold´ an, Phys. Rev. X12, 041026 (2022)

    work page 2022

  34. [34]

    I. A. Mart´ ınez, G. Bisker, J. M. Horowitz, and J. M. R. Parrondo, Nat. Commun.10, 3542 (2019)

    work page 2019

  35. [35]

    Bisker, M

    G. Bisker, M. Polettini, T. R. Gingrich, and J. M. Horowitz, J. Stat. Mech. , 093210 (2017)

    work page 2017

  36. [36]

    Polettini and M

    M. Polettini and M. Esposito, Phys. Rev. Lett.119, 240601 (2017)

    work page 2017

  37. [37]

    van der Meer, J

    J. van der Meer, J. Deg¨ unther, and U. Seifert, Phys. Rev. Lett.130, 257101 (2023)

    work page 2023

  38. [38]

    Pietzonka and F

    P. Pietzonka and F. Coghi, Phys. Rev. E109, 064128 (2024)

    work page 2024

  39. [39]

    Ehrich, J

    J. Ehrich, J. Stat. Mech. , P083214 (2021)

    work page 2021

  40. [40]

    Nitzan, A

    E. Nitzan, A. Ghosal, and G. Bisker, Phys. Rev. Res.5, 043251 (2023)

    work page 2023

  41. [41]

    Knotz, T

    G. Knotz, T. M. Muenker, T. Betz, and M. Kr¨ uger, Front. Phys.11, 1331835 (2024). 12

    work page 2024

  42. [42]

    Aguilera, S

    M. Aguilera, S. Ito, and A. Kolchinsky, Phys. Rev. Lett.136, 077101 (2026)

    work page 2026

  43. [43]

    S. Ro, B. Guo, A. Shih, T. V. Phan, R. H. Austin, D. Levine, P. M. Chaikin, and S. Martiniani, Phys. Rev. Lett.129, 220601 (2022)

    work page 2022

  44. [44]

    D.-K. Kim, Y. Bae, S. Lee, and H. Jeong, Phys. Rev. Lett.125, 140604 (2020)

    work page 2020

  45. [45]

    N. M. Boffi and E. Vanden-Eijnden, Proc. Natl. Acad. Sci. U.S.A.121, e2318106121 (2024)

    work page 2024