Pith. sign in

REVIEW 2 major objections 3 minor 78 references

Quantifying dissipation in flocking dynamics: When tracking internal states matters

T0 review · 2 major / 3 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read In flocking, hidden internal states carry most of the energy cost when order is weak.

desk verdict A useful thermodynamically consistent flocking model, but the central dissipation crossover is undercut by the paper's own hydrodynamics and needs finite-size scaling. read the letter →

arxiv 2505.13113 v2 pith:I75ZJFZK submitted 2025-05-19 cond-mat.stat-mech

Karel Proesmans , Gianmaria Falasco , Atul Tanaji Mohite , Massimiliano Esposito , Étienne Fodor This is my paper · ORCID
classification cond-mat.stat-mech
keywords activematterflockingtransitionentropyproductionratelocaldetailedbalancecoarsegrainingIsingmodelstochasticthermodynamicsreaction-diffusionsystems
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 builds a thermodynamically consistent lattice model of flocking in which each particle's internal state biases its diffusion and both state changes and spatial jumps obey local detailed balance with respect to the same interaction energy. Using this model, it establishes a crossover in the entropy production rate: in the weakly interacting apolar phase the dissipation is maximal, equal to the non-interacting value, while any inference that discards internal state dynamics predicts a vanishing entropy production; in the strongly interacting polar phase dissipation is lower and the same partial inference captures most of it. It then coarse-grains the model to hydrodynamics and shows the macroscopic entropy production equals the microscopic one, through a mapping to non-ideal reaction-diffusion systems. A sympathetic reader would care because it tells experimenters when trajectory data that hides self-propulsion direction will mislead energy accounting, and when it will not.

What carries the argument

The load-bearing object is a lattice model of $N$ particles with two internal states $+,-$, with interaction energy $E$ built from local density and polarization, and transition rates for state flips and site jumps set by local detailed balance with respect to the same $E$. This thermodynamic consistency is what lets the entropy production rate be computed exactly as $T\dot{S}=\Delta\mu\langle J_p-J_m\rangle$ in steady state. The inference machinery consists of coarse-graining tracer jump rates from waiting times: keeping internal states gives $\dot{S}_{\mathrm{I}}$, discarding them gives $\dot{S}_{\mathrm{II}}$, with the chain $0\le\dot{S}_{\mathrm{II}}\le\dot{S}_{\mathrm{I}}\le\dot{S}$. The hydrodynamic step uses a path-integral coarse-graining to non-ideal reaction-diffusion equations in $(\rho,P)$, whose dissipative and reactive contributions reproduce the microscopic entropy production.

What would settle it

Measure the true dissipation from fuel consumption, namely the $\Delta\mu$ current, in a thermodynamically consistent flocking model or in chemically driven self-propelled particles while simultaneously recording trajectories that hide the internal propulsion state. In the apolar phase the paper predicts the hidden-state inference will report near-zero entropy production while the fuel-based measurement stays at the non-interacting maximum; an experiment that finds comparable inferred and true rates in apolar conditions would falsify the crossover.

Watch

Extended reading notes

Core claim

The central claim is that in a thermodynamically consistent version of the active Ising model, the entropy production rate $\dot{S}$ is not largest at the flocking transition but in the disordered apolar phase, where $\dot{S}=N\gamma\Delta\mu^2/T$ exactly as for non-interacting particles. Partial inference that follows only positions, $\dot{S}_{\mathrm{II}}$, vanishes in that phase even though true dissipation is high; by contrast, in the polar phase $\dot{S}$ is reduced and $\dot{S}_{\mathrm{II}}$ approaches it. The paper also proves that the hydrodynamic entropy production $\dot{S}_{\mathrm{macro}}$ equals the microscopic $\dot{S}$ under coarse-graining, giving $T\dot{S}_{\mathrm{macro}}=(D/T)\rho_0 V f^2$ in homogeneous phases, and identifies the reason as the mapping of active lattice models with local detailed balance to a class of non-ideal reaction-diffusion systems.

Load-bearing premise

The inference estimates assume each tracer's jump dynamics is Markovian and spatially uniform; the paper itself reports waiting-time distributions with non-exponential tails in the polar phase and deliberately ignores spatial inhomogeneities, so if tracer dynamics is strongly non-Markovian the inferred entropy productions are no longer guaranteed bounds and the crossover could be distorted.

Editorial extensions

If this is right

  • Direct steady-state entropy production is accessible exactly as $\Delta\mu$ times the net current of $+$ and $-$ particles, so energy accounting in thermodynamically consistent active lattice models can be done without fluctuating-force approximations.
  • In apolar or weakly ordered flocks, any dissipation estimate based only on visible displacements will severely undercount energy expenditure; hidden internal-state dynamics are the dominant dissipative channel.
  • In polar flocks, position-only tracking is sufficient: the inferred rate $\dot{S}_{\mathrm{II}}$ approaches the true $\dot{S}$, so experiments can trust displacement data there.
  • The macroscopic hydrodynamic entropy production reproduces the microscopic value, so coarse-grained descriptions of active matter do not lose dissipative content if the coarse-graining keeps both the diffusive and reactive sectors.
  • The inferred entropy production without internal states scales with the square of polarization, $\dot{S}_{\mathrm{II,macro}}\propto P_0^2/\rho_0$, giving a quantitative link between macroscopic order and apparent dissipation.

Reading between the lines

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

  • A natural experimental test would compare fuel consumption with orientation-hidden trajectory inference in colloidal or bacterial flocks; the model predicts the two agree only when global polarization is high.
  • The mapping to non-ideal reaction-diffusion systems implies the same inference gap should appear in any chemically driven system whose hidden internal coordinate is tightly coupled to transport, not just in flocking.
  • If non-Markovian waiting times in the coexistence phase are generic, then band-forming regimes are where partial inference is least reliable; direct current measurements, not waiting-time estimates, would be needed there.
  • The plateau of maximal dissipation in the disordered phase suggests that adding alignment reduces dissipation per particle, so flocking order could be viewed as an energy-saving collective state rather than a costly one.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 3 minor

Summary. The paper introduces a thermodynamically consistent lattice model of flocking in which particles carry two internal states (+/−) that bias their diffusion, and both state flips and lattice jumps obey local detailed balance with respect to the same interaction energy. The authors map out the apolar/coexistence/polar phase diagram, compute the exact microscopic entropy production rate (EPR), and compare it with two coarse-grained inference schemes that either track or discard internal states. Their central numerical finding is a crossover: in the apolar phase the EPR is maximal and equals the non-interacting value while the inference that discards internal states predicts a vanishing EPR; in the polar phase the EPR is reduced and the same partial inference captures most of the dissipation. The paper then derives a hydrodynamic description in the macroscopic limit and claims that the macroscopic EPR coincides with the microscopic EPR, connecting the model to a class of non-ideal reaction-diffusion systems.

Significance. If the crossover claim is robust, the paper makes a valuable contribution: it provides a thermodynamically consistent alternative to the active Ising model, gives an exact microscopic EPR formula, and demonstrates in a minimal setting that partial inference can severely misestimate dissipation when internal degrees of freedom are discarded. The mapping to non-ideal reaction-diffusion systems is elegant and connects active lattice models to a broader thermodynamic framework. The strengths include the explicit local- detailed-balance construction, the exact steady-state EPR expression in Eq. (10), and the clear identification of a regime where internal-state tracking is essential. However, the central crossover is currently undermined by the paper's own hydrodynamic calculation, which yields an EPR independent of interaction strength, so the significance is contingent on resolving that mismatch.

major comments (2)
  1. [§III B, Eq. (38)] The central crossover claim of the abstract and Sec. II D 3—that dissipation is reduced in the polar phase—is contradicted by the paper's own macroscopic calculation. Equation (38) gives T\dot S_macro = (D/T) ρ0 V f^2, which is independent of ε, and the text concedes that the hydrodynamics 'does not reproduce the variation of EPR reported in the lattice model [Fig. 3].' Thus the reduction seen in Fig. 3 is, within the paper's own analysis, a finite-size or fluctuation effect. Because no system-size dependence, finite-size scaling, or error bars are reported for Fig. 3, the crossover cannot be distinguished from a finite-size artifact. Please provide a system-size analysis (e.g., n-dependence of the EPR at fixed ε and ρ0) or an explicit argument for why the macroscopic limit should not be used to assess the polar-phase dissipation.
  2. [§II D 1, Fig. 4] The inference schemes S_I and S_II assume that each particle's jump and flip rates are Markovian and site-independent, with rates extracted from average waiting times. The paper itself shows in Fig. 4 that waiting-time distributions deviate from exponential tails in the polar phase, and the text acknowledges that spatial inhomogeneities are discarded. If the effective tracer dynamics is non-Markovian, the coarse-grained bounds 0 ≤ S_II ≤ S_I ≤ S in Eq. (15) do not strictly apply, and the conclusion that S_II ≃ S deep in the polar phase may be an artifact of the exponential-fit procedure. Please quantify the deviation from exponentiality and its effect on the inferred rates, or restrict the claim to the regime in which the Markovian approximation is explicitly validated.
minor comments (3)
  1. [§IV] The sentence 'for strong interactions, the EPR can be accurately inferred ... for strong interactions, such an inference severely underestimates the EPR' repeats 'strong interactions' twice; the second instance should clearly read 'weak interactions.'
  2. [§II A, Eq. (2)] The interaction energy E contains terms such as P^2/ρ and P/√ρ, which are singular when a lattice site is empty (ρ=0). The model allows arbitrary occupancy, so the paper should state the convention used to define E (or the rates) at empty sites; otherwise the numerical implementation is not fully specified.
  3. [Fig. 3 and Fig. 4] Neither figure reports error bars or the number of independent runs, even though the central quantitative claims (e.g., S_II ≃ S in the polar phase) rely on the closeness of numerical estimates. Please include at least representative statistical uncertainties.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the microscopic and macroscopic EPR derivations are self-contained, and the self-citations are supporting rather than load-bearing.

full rationale

I walked the derivation chain and found no step in which a claimed prediction reduces by construction to its inputs. The microscopic EPR in Eq. (6) is the standard stochastic-thermodynamics definition, and Eq. (10), T\dot S = \Delta\mu\langle J_p-J_m\rangle_{ss}, follows directly from local detailed balance and the definition of active work; no target result is inserted into the definition. The inferred EPRs in Eqs. (12)-(13) are defined from measured jump rates, and the ordering 0\le \dot S_{II}\le \dot S_I\le \dot S is a coarse-graining property cited from Refs. [36,55]; the comparison with the direct EPR is an empirical comparison, not a fit of the direct EPR. The macroscopic EPR in Eqs. (32)-(33) is the standard non-ideal reaction-diffusion decomposition, and the micro-macro correspondence in Eqs. (35)-(37) is derived through the continuum limit of the active current and the free-energy balance, not assumed. The self-citations to Refs. [50,57-59] supply the generic reaction-diffusion framework, but the present paper rederives the needed hydrodynamic relations in Sec. III and Appendix A, so no load-bearing argument reduces to an unverified self-citation. The paper also explicitly flags its own limitation: 'Since our hydrodynamics only features a homogeneous steady state, it does not reproduce the variation of EPR reported in the lattice model [Fig. 3]' (Sec. III B), and Fig. 4 shows non-exponential waiting-time tails in the polar phase. These are internal limitations or correctness risks for the finite-size crossover claim, not circularity, because the numerical EPR is not defined in terms of the inferred EPR or the hydrodynamic EPR.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The model has control parameters (epsilon, epsilon_0, nu, gamma, Delta-mu, T) but these are not fitted to data or adjusted to force the results; there are no hidden free parameters in the derivations. The main axioms are standard stochastic thermodynamics assumptions plus the specific choice of interaction energy and the coarse-graining approximations. No new physical entities are introduced.

assumptions (5)
  • domain assumption Local detailed balance for internal-state transitions and site jumps with respect to the same interaction energy (Eqs. 4-5).
    This thermodynamic consistency condition makes the entropy production rate well-defined; it is a standard postulate in stochastic thermodynamics.
  • domain assumption Tight coupling between chemical fuel consumption and each biased jump (Sec. II A).
    Each product consumption is associated with one biased jump, setting the chemical potential difference Delta-mu as the affinity per jump.
  • ad hoc to paper Specific form of interaction energy E with local and nearest-neighbor aligning terms (Eq. 2).
    This is a model choice, not derived; it is chosen to reproduce the three flocking phases (apolar, coexistence, polar).
  • domain assumption Macroscopic limit discards field fluctuations and expands jump rates to first order in lattice spacing (Appendix A, Eq. A3).
    This is a standard mean-field coarse-graining, but it may neglect interaction-induced mobility corrections that could affect the correspondence between micro and macro EPR.
  • ad hoc to paper Tracer dynamics is Markovian and site-independent for the inference scheme (Sec. II D 1).
    Waiting-time distributions deviate from exponential in the polar-phase tails (Fig. 4), so this approximation is not exact and is only numerically justified.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantifying dissipation in flocking dynamics: When tracking internal states matters." pith.science (2026). https://pith.science/paper/I75ZJFZK

@misc{pith2026250513113,
  author       = {Pith},
  title        = {Pith review of: Quantifying dissipation in flocking dynamics: When tracking internal states matters},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I75ZJFZK}},
  note         = {Machine review of arXiv:2505.13113}
}
read the original abstract

Aligning self-propelled particles undergo a nonequilibrium flocking transition from apolar to polar phases as their interactions become stronger. We propose a thermodynamically consistent lattice model, in which the internal state of the particles biases their diffusion, to capture such a transition. Changes of internal states and jumps between lattice sites obey local detailed balance with respect to the same interaction energy. We unveil a crossover between two regimes: for weak interactions, the dissipation is maximal, and partial inference (namely, based on discarding the dynamics of internal states) leads to a severe underestimation; for strong interactions, the dissipation is reduced, and partial inference captures most of the dissipation. Finally, we reveal that the macroscopic dissipation, evaluated at the hydrodynamic level, coincides with the microscopic dissipation upon coarse-graining. We argue that this correspondence stems from a generic mapping of active lattice models with local detailed balance into a specific class of non-ideal reaction-diffusion systems.

Figures

Figures reproduced from arXiv: 2505.13113 by the authors.

Figure 1
Figure 1. FIG. 1. Self-propelled particles (+ [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Phase diagram of lattice model as a function of align [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Entropy production rate (EPR) per particle, and [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Probability distribution [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

78 extracted references · 69 canonical work pages

  1. [1]

    Specifically, our aim is to re- duce our many-body dynamics [Eq

    Tracking internal states Inspired by [53, 54], we explore under which conditions the EPR can be inferred from the dynamics of a tracer embedded in the system. Specifically, our aim is to re- duce our many-body dynamics [Eq. (1)] into the dynam- ics of some representative particles for each state (+,−). To this end, we consider the rate js↑ at which partic...

    work page

  2. [2]

    The in- ferred EPR correspondingly reads ˙SII = (j↑−j↓) lnj↑ j↓ + (j←−j→) lnj← j→ , (13) where j↑ = X s∈(+,−) js↑, (14) and a similar definition holds for ( j↓,j←,j→)

    Discarding internal states Assuming that one cannot track internal states, the tracer dynamics is then prescribed by effective transition rates which do not distinguish (+ ,−) particles. The in- ferred EPR correspondingly reads ˙SII = (j↑−j↓) lnj↑ j↓ + (j←−j→) lnj← j→ , (13) where j↑ = X s∈(+,−) js↑, (14) and a similar definition holds for ( j↓,j←,j→). Th...

    work page

  3. [3]

    (12)] is rather close to the original ˙S [Eq

    What do we learn from inference? Overall, our results show that the inferred EPR ˙SI [Eq. (12)] is rather close to the original ˙S [Eq. (6)] in all phases: when tracking internal states, our inference method provides a satisfactory estimation. Instead, a significant discrepancy arises when discarding internal states [ ˙SII, Eq. (13)]. By definition, ˙SII ...

    work page arXiv

  4. [4]

    Hydrodynamics of soft active matter,

    M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, Madan Rao, and R. Aditi Simha, “Hydrodynamics of soft active matter,” Rev. Mod. Phys. 85, 1143–1189 (2013)

    2013

  5. [5]

    Active particles in complex and crowded environments,

    Clemens Bechinger, Roberto Di Leonardo, Hartmut L¨ owen, Charles Reichhardt, Giorgio Volpe, and Gio- vanni Volpe, “Active particles in complex and crowded environments,” Rev. Mod. Phys. 88, 045006 (2016)

    work page 2016

  6. [6]

    The statisti- cal physics of active matter: From self-catalytic colloids to living cells,

    ´Etienne Fodor and M. Cristina Marchetti, “The statisti- cal physics of active matter: From self-catalytic colloids to living cells,” Phys. A: Stat. Mech. Appl. 504, 106–120 (2018)

    work page 2018

  7. [7]

    Living crystals of light-activated colloidal surfers,

    J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, “Living crystals of light-activated colloidal surfers,” Science 339, 936–940 (2013)

    work page 2013

  8. [8]

    Emergence of macroscopic directed motion in popula- tions of motile colloids,

    Antoine Bricard, Jean-Baptiste Caussin, Nicolas Desreumaux, Olivier Dauchot, and Denis Bartolo, “Emergence of macroscopic directed motion in popula- tions of motile colloids,” Nature 503, 95–98 (2013)

    work page 2013

Show all 78 references
  1. [9]

    Physics of mi- croswimmers—single particle motion and collective be- havior: a review,

    J Elgeti, R G Winkler, and G Gompper, “Physics of mi- croswimmers—single particle motion and collective be- havior: a review,” Rep. Prog. Phys. 78, 056601 (2015)

    2015

  2. [10]

    Long-Range Order in a Two- Dimensional Dynamical XY Model: How Birds Fly To- gether,

    John Toner and Yuhai Tu, “Long-Range Order in a Two- Dimensional Dynamical XY Model: How Birds Fly To- gether,” Phys. Rev. Lett. 75, 4326–4329 (1995)

    1995

  3. [11]

    Novel type of phase tran- sition in a system of self-driven particles,

    Tam´ as Vicsek, Andr´ as Czir´ ok, Eshel Ben-Jacob, Inon Cohen, and Ofer Shochet, “Novel type of phase tran- sition in a system of self-driven particles,” Phys. Rev. Lett. 75, 1226–1229 (1995)

    1995

  4. [12]

    Dry aligning dilute active matter,

    H. Chat´ e, “Dry aligning dilute active matter,” Annu. Rev. Condens. Matter Phys. 11, 189–212 (2020)

    2020

  5. [13]

    Motility-induced phase separation,

    Michael E. Cates and Julien Tailleur, “Motility-induced phase separation,” Annu. Rev. Condens. Matter Phys. 6, 219–244 (2015)

    2015

  6. [14]

    Irreversibility and biased ensembles in active matter: Insights from stochastic thermodynamics,

    ´Etienne Fodor, Robert L. Jack, and Michael E. Cates, “Irreversibility and biased ensembles in active matter: Insights from stochastic thermodynamics,” Annu. Rev. Condens. Matter Phys. 13, 215–238 (2022)

    2022

  7. [15]

    Time irreversibility in active matter, from micro to macro,

    J. O’Byrne, Y. Kafri, J. Tailleur, and F. van Wij- land, “Time irreversibility in active matter, from micro to macro,” Nat. Rev. Phys. 4, 167–183 (2022)

    2022

  8. [16]

    How far from equilibrium is active matter?

    ´Etienne Fodor, Cesare Nardini, Michael E. Cates, Julien Tailleur, Paolo Visco, and Fr´ ed´ eric van Wijland, “How far from equilibrium is active matter?” Phys. Rev. Lett. 117, 038103 (2016)

    2016

  9. [17]

    Statistical mechanics of active ornstein-uhlenbeck particles,

    David Martin, J´ er´ emy O'Byrne, Michael E. Cates, ´Etienne Fodor, Cesare Nardini, Julien Tailleur, and Fr´ ed´ eric van Wijland, “Statistical mechanics of active ornstein-uhlenbeck particles,” Phys. Rev. E 103, 032607 (2021)

    2021

  10. [18]

    En- tropy production in field theories without time-reversal symmetry: Quantifying the non-equilibrium character of active matter,

    Cesare Nardini, ´Etienne Fodor, Elsen Tjhung, Fr´ ed´ eric van Wijland, Julien Tailleur, and Michael E. Cates, “En- tropy production in field theories without time-reversal symmetry: Quantifying the non-equilibrium character of active matter,” Phys. Rev. X 7, 021007 (2017)

    2017

  11. [19]

    Time-reversal symmetry violations and entropy produc- tion in field theories of polar active matter,

    Øyvind L Borthne, ´Etienne Fodor, and Michael E Cates, “Time-reversal symmetry violations and entropy produc- tion in field theories of polar active matter,” New J. Phys. 22, 123012 (2020)

    2020

  12. [20]

    Irreversible mesoscale fluctuations herald the emergence of dynamical phases,

    Thomas Suchanek, Klaus Kroy, and Sarah A. M. Loos, “Irreversible mesoscale fluctuations herald the emergence of dynamical phases,” Phys. Rev. Lett. 131, 258302 (2023)

    2023

  13. [21]

    Irreversibility across a nonreciprocal PT -symmetry- breaking phase transition,

    Henry Alston, Luca Cocconi, and Thibault Bertrand, “Irreversibility across a nonreciprocal PT -symmetry- breaking phase transition,” Phys. Rev. Lett. 131, 258301 (2023)

    2023

  14. [22]

    Active engines: Thermodynamics moves forward,

    ´Etienne Fodor and Michael E. Cates, “Active engines: Thermodynamics moves forward,” Europhys. Lett. 134, 10003 (2021)

    2021

  15. [23]

    Efficiency of isothermal active matter engines: Strong driving beats weak driving,

    Thomas Speck, “Efficiency of isothermal active matter engines: Strong driving beats weak driving,” Phys. Rev. E 105, L012601 (2022)

    2022

  16. [24]

    Active matter under control: Insights from response theory,

    Luke K. Davis, Karel Proesmans, and ´Etienne Fodor, “Active matter under control: Insights from response theory,” Phys. Rev. X 14, 011012 (2024)

    2024

  17. [25]

    Optimal control in soft and active matter,

    Jos´ e Alvarado, Erin Teich, David Sivak, and John Bech- hoefer, “Optimal control in soft and active matter,” (2025), arXiv:2504.08676 [cond-mat.soft]

    2025 arXiv

  18. [26]

    Physical bioenergetics: Energy fluxes, budgets, and constraints in cells,

    Xingbo Yang, Matthias Heinemann, Jonathon Howard, Greg Huber, Srividya Iyer-Biswas, Guillaume Le Treut, Michael Lynch, Kristi L. Montooth, Daniel J. Needle- man, Simone Pigolotti, Jonathan Rodenfels, Pierre Ron- ceray, Sadasivan Shankar, Iman Tavassoly, Shashi Thutu- palli, De...

    2021

  19. [27]

    Dissipation and energy propagation across scales in an active cytoskeletal material,

    Peter J. Foster, Jinhye Bae, Bezia Lemma, Juanjuan Zheng, William Ireland, Pooja Chandrakar, R´ emi Boros, Zvonimir Dogic, Daniel J. Needleman, and Joost J. Vlas- sak, “Dissipation and energy propagation across scales in an active cytoskeletal material,” Proc. Natl. Acad. Sci....

    2023

  20. [28]

    Entropy production of active particles and for particles in active baths,

    Patrick Pietzonka and Udo Seifert, “Entropy production of active particles and for particles in active baths,” J. 10 Phys. A: Math. Theor. 51, 01LT01 (2017)

    2017

  21. [29]

    Active brownian particles driven by con- stant affinity,

    Thomas Speck, “Active brownian particles driven by con- stant affinity,” Europhys. Lett. 123, 20007 (2018)

    2018

  22. [30]

    Thermodynamics and statistical mechanics of chemically powered synthetic nanomotors,

    Pierre Gaspard and Raymond Kapral, “Thermodynamics and statistical mechanics of chemically powered synthetic nanomotors,” Adv. Phys.: X 4, 1602480 (2019)

    2019

  23. [31]

    Enhanced dif- fusivity in microscopically reversible active matter,

    Artem Ryabov and Mykola Tasinkevych, “Enhanced dif- fusivity in microscopically reversible active matter,” Soft Matter 18, 3234–3240 (2022)

    2022

  24. [32]

    Thermodynamically consistent model of an active ornstein–uhlenbeck particle,

    J H Fritz and U Seifert, “Thermodynamically consistent model of an active ornstein–uhlenbeck particle,” J. Stat. Mech. 2023, 093204 (2023)

    2023

  25. [33]

    Thermodynamics of active matter: Tracking dissipation across scales,

    Robin Bebon, Joshua F. Robinson, and Thomas Speck, “Thermodynamics of active matter: Tracking dissipation across scales,” Phys. Rev. X 15, 021050 (2025)

    2025

  26. [34]

    Entropy production and thermodynamic inference for stochastic microswimmers,

    Michalis Chatzittofi, Jaime Agudo-Canalejo, and Ramin Golestanian, “Entropy production and thermodynamic inference for stochastic microswimmers,” Phys. Rev. Res. 6, L022044 (2024)

    2024

  27. [35]

    Ther- modynamically consistent lattice monte carlo method for active particles,

    Ki-Won Kim, Euijoon Kwon, and Yongjoo Baek, “Ther- modynamically consistent lattice monte carlo method for active particles,” (2025), arXiv:2503.16958 [cond- mat.soft]

    2025 arXiv

  28. [36]

    Thermodynamics of active field theo- ries: Energetic cost of coupling to reservoirs,

    Tomer Markovich, ´Etienne Fodor, Elsen Tjhung, and Michael E. Cates, “Thermodynamics of active field theo- ries: Energetic cost of coupling to reservoirs,” Phys. Rev. X 11, 021057 (2021)

    2021

  29. [37]

    A gallavotti– cohen-type symmetry in the large deviation functional for stochastic dynamics,

    Joel L Lebowitz and Herbert Spohn, “A gallavotti– cohen-type symmetry in the large deviation functional for stochastic dynamics,” J. Stat. Phys. 95, 333–365 (1999)

    1999

  30. [38]

    Stochastic thermodynamics, fluctuation theorems and molecular machines,

    Udo Seifert, “Stochastic thermodynamics, fluctuation theorems and molecular machines,” Rep. Prog. Phys.75, 126001 (2012)

    2012

  31. [39]

    Ensemble and tra- jectory thermodynamics: A brief introduction,

    C. Van den Broeck and M. Esposito, “Ensemble and tra- jectory thermodynamics: A brief introduction,” Phys. A: Stat. Mech. Appl. 418, 6–16 (2015)

    2015

  32. [40]

    Aggregation and sedimentation of active Brownian par- ticles at constant affinity,

    Andreas Fischer, Arkya Chatterjee, and Thomas Speck, “Aggregation and sedimentation of active Brownian par- ticles at constant affinity,” J. Chem. Phys. 150, 064910 (2019)

    2019

  33. [41]

    Revisiting the Flocking Transition Using Active Spins,

    A. P. Solon and J. Tailleur, “Revisiting the Flocking Transition Using Active Spins,” Phys. Rev. Lett. 111, 078101 (2013)

    2013

  34. [42]

    Flocking with discrete sym- metry: The two-dimensional active ising model,

    A. P. Solon and J. Tailleur, “Flocking with discrete sym- metry: The two-dimensional active ising model,” Phys. Rev. E 92, 042119 (2015)

    2015

  35. [43]

    Flocking and reorientation transition in the 4-state active potts model,

    Swarnajit Chatterjee, Matthieu Mangeat, Raja Paul, and Heiko Rieger, “Flocking and reorientation transition in the 4-state active potts model,” Europhys. Lett. 130, 66001 (2020)

    2020

  36. [44]

    Flip motion of solitary wave in an ising-type vicsek model,

    Hidetsugu Sakaguchi and Kazuya Ishibashi, “Flip motion of solitary wave in an ising-type vicsek model,” Phys. Rev. E 100, 052113 (2019)

    2019

  37. [45]

    Non-reciprocal interactions spatially propagate fluctua- tions in a 2d ising model,

    Daniel S Seara, Akash Piya, and A Pasha Tabatabai, “Non-reciprocal interactions spatially propagate fluctua- tions in a 2d ising model,” J. Stat. Mech. 2023, 043209 (2023)

    2023

  38. [46]

    Active ising models of flocking: a field-theoretic approach,

    Mattia Scandolo, Johannes Pausch, and Michael E Cates, “Active ising models of flocking: a field-theoretic approach,” Eur. Phys. J. E 46, 103 (2023)

    2023

  39. [47]

    Susceptibility of polar flocks to spatial anisotropy,

    Alexandre Solon, Hugues Chat´ e, John Toner, and Julien Tailleur, “Susceptibility of polar flocks to spatial anisotropy,” Phys. Rev. Lett. 128, 208004 (2022)

    2022

  40. [48]

    Fluctuation-induced phase separation in metric and topological models of collective motion,

    David Martin, Hugues Chat´ e, Cesare Nardini, Alexan- dre Solon, Julien Tailleur, and Fr´ ed´ eric Van Wijland, “Fluctuation-induced phase separation in metric and topological models of collective motion,” Phys. Rev. Lett. 126, 148001 (2021)

    2021

  41. [49]

    The interplay of diffusion and heterogeneity in nucleation of the net- worked ising model,

    Chuansheng Shen and Hanshuang Chen, “The interplay of diffusion and heterogeneity in nucleation of the net- worked ising model,” Commun. Theor. Phys. 73, 115601 (2021)

    2021

  42. [50]

    Numerical treatment of the boltzmann equation for self-propelled particle systems,

    Florian Th¨ uroff, Christoph A. Weber, and Erwin Frey, “Numerical treatment of the boltzmann equation for self-propelled particle systems,” Phys. Rev. X 4, 041030 (2014)

    2014

  43. [51]

    Inter- pretable machine learning for inferring the phase bound- aries in a nonequilibrium system,

    C. Casert, T. Vieijra, J. Nys, and J. Ryckebusch, “Inter- pretable machine learning for inferring the phase bound- aries in a nonequilibrium system,” Phys. Rev. E 99, 023304 (2019)

    2019

  44. [52]

    Local detailed balance,

    Christian Maes, “Local detailed balance,” SciPost Phys. Lect. Notes , 32 (2021)

    2021

  45. [53]

    Thermodynamically consistent flocking: from discontinuous to continuous transitions,

    Tal Agranov, Robert L Jack, Michael E Cates, and ´Etienne Fodor, “Thermodynamically consistent flocking: from discontinuous to continuous transitions,” New J. Phys. 26, 063006 (2024)

    2024

  46. [54]

    A general method for numerically simulating the stochastic time evolution of coupled chem- ical reactions,

    Daniel T Gillespie, “A general method for numerically simulating the stochastic time evolution of coupled chem- ical reactions,” Journal of Computational Physics 22, 403–434 (1976)

    1976

  47. [55]

    Energy cost for flocking of ac- tive spins: The cusped dissipation maximum at the flock- ing transition,

    Qiwei Yu and Yuhai Tu, “Energy cost for flocking of ac- tive spins: The cusped dissipation maximum at the flock- ing transition,” Phys. Rev. Lett. 129, 278001 (2022)

    2022

  48. [56]

    Decomposing the local arrow of time in interacting systems,

    Christopher W. Lynn, Caroline M. Holmes, William Bialek, and David J. Schwab, “Decomposing the local arrow of time in interacting systems,” Phys. Rev. Lett. 129, 118101 (2022)

    2022

  49. [57]

    Emergence of local ir- reversibility in complex interacting systems,

    Christopher W. Lynn, Caroline M. Holmes, William Bialek, and David J. Schwab, “Emergence of local ir- reversibility in complex interacting systems,” Phys. Rev. E 106, 034102 (2022)

    2022

  50. [58]

    Stochastic thermodynamics un- der coarse graining,

    Massimiliano Esposito, “Stochastic thermodynamics un- der coarse graining,” Phys. Rev. E 85, 041125 (2012)

    2012

  51. [59]

    Macro- scopic stochastic thermodynamics,

    Gianmaria Falasco and Massimiliano Esposito, “Macro- scopic stochastic thermodynamics,” Rev. Mod. Phys. 97, 015002 (2025)

    2025

  52. [60]

    Nonequilibrium thermody- namics of non-ideal reaction–diffusion systems: Implica- tions for active self-organization,

    Francesco Avanzini, Timur Aslyamov, ´Etienne Fodor, and Massimiliano Esposito, “Nonequilibrium thermody- namics of non-ideal reaction–diffusion systems: Implica- tions for active self-organization,” J. Chem. Phys. 161, 174108 (2024)

    2024

  53. [61]

    Nonideal Reaction- Diffusion Systems: Multiple Routes to Instability,

    Timur Aslyamov, Francesco Avanzini, ´Etienne Fodor, and Massimiliano Esposito, “Nonideal Reaction- Diffusion Systems: Multiple Routes to Instability,” Phys. Rev. Lett. 131, 138301 (2023)

    2023

  54. [62]

    Entropy production rate in thermody- namically consistent flocks,

    Tal Agranov, Robert L. Jack, Michael E. Cates, and ´Etienne Fodor, “Entropy production rate in thermody- namically consistent flocks,” (2025), arXiv:2505.13117 [cond-mat.stat-mech]

    2025

  55. [63]

    Origins and diagnostics of the nonequilib- rium character of active systems,

    Lokrshi Prawar Dadhichi, Ananyo Maitra, and Sriram Ramaswamy, “Origins and diagnostics of the nonequilib- rium character of active systems,” J. Stat. Mech. 2018, 123201 (2018)

    2018

  56. [64]

    Signatures of irreversibility 11 in microscopic models of flocking,

    Federica Ferretti, Simon Grosse-Holz, Caroline Holmes, Jordan L. Shivers, Irene Giardina, Thierry Mora, and Aleksandra M. Walczak, “Signatures of irreversibility 11 in microscopic models of flocking,” Phys. Rev. E 106, 034608 (2022)

    2022

  57. [65]

    Out of equilibrium response and fluctuation-dissipation violations across scales in flocking systems,

    Federica Ferretti, Irene Giardina, Tomas Grigera, Giu- lia Pisegna, and Mario Veca, “Out of equilibrium response and fluctuation-dissipation violations across scales in flocking systems,” (2024), arXiv:2405.12874 [cond-mat.stat-mech]

    2024 arXiv

  58. [66]

    Model-free learning of probability flows: Elucidating the nonequi- librium dynamics of flocking,

    Nicholas M. Boffi and Eric Vanden-Eijnden, “Model-free learning of probability flows: Elucidating the nonequi- librium dynamics of flocking,” (2024), arXiv:2411.14317 [cond-mat.stat-mech]

    2024 arXiv

  59. [67]

    Nonreciprocal ising model,

    Yael Avni, Michel Fruchart, David Martin, Daniel Seara, and Vincenzo Vitelli, “Nonreciprocal ising model,” Phys. Rev. Lett. 134, 117103 (2025)

    2025

  60. [68]

    Long-range order and directional defect prop- agation in the nonreciprocal XY model with vision cone interactions,

    Sarah A. M. Loos, Sabine H. L. Klapp, and Thomas Martynec, “Long-range order and directional defect prop- agation in the nonreciprocal XY model with vision cone interactions,” Phys. Rev. Lett. 130, 198301 (2023)

    2023

  61. [69]

    Flocking of two unfriendly species: The two-species vicsek model,

    Swarnajit Chatterjee, Matthieu Mangeat, Chul-Ung Woo, Heiko Rieger, and Jae Dong Noh, “Flocking of two unfriendly species: The two-species vicsek model,” Phys. Rev. E 107, 024607 (2023)

    2023

  62. [70]

    Inescapable anisotropy of non- reciprocal xy models,

    Dawid Dopierala, Hugues Chat´ e, Xia qing Shi, and Alexandre Solon, “Inescapable anisotropy of non- reciprocal xy models,” (2025), arXiv:2503.14466 [cond- mat.stat-mech]

    2025 arXiv

  63. [71]

    Stochastic ther- modynamics of non-reciprocally interacting particles and fields,

    Atul Tanaji Mohite and Heiko Rieger, “Stochastic ther- modynamics of non-reciprocally interacting particles and fields,” (2025), arXiv:2504.10515 [cond-mat.stat-mech]

    2025 arXiv

  64. [72]

    Pulsating active mat- ter,

    Yiwei Zhang and ´Etienne Fodor, “Pulsating active mat- ter,” Phys. Rev. Lett. 131, 238302 (2023)

    2023

  65. [73]

    Diffusive os- cillators capture the pulsating states of deformable par- ticles,

    Alessandro Manacorda and ´Etienne Fodor, “Diffusive os- cillators capture the pulsating states of deformable par- ticles,” Phys. Rev. E 111, L053401 (2025)

    2025

  66. [74]

    Hydrodynamics of pulsating active liquids,

    Tirthankar Banerjee, Thibault Desaleux, Jonas Ranft, and ´Etienne Fodor, “Hydrodynamics of pulsating active liquids,” (2024), arXiv:2407.19955 [cond-mat.soft]

    2024

  67. [75]

    Calorimetry for active systems,

    Pritha Dolai, Christian Maes, and Karel Netoˇ cn´ y, “Calorimetry for active systems,” SciPost Phys. 14, 126 (2023)

    2023

  68. [76]

    Lattice models of nonequilibrium bacterial dynamics,

    A G Thompson, J Tailleur, M E Cates, and R A Blythe, “Lattice models of nonequilibrium bacterial dynamics,” J. Stat. Mech. 2011, P02029 (2011)

    2011

  69. [77]

    Exact fluctuating hydrodynamics of active lat- tice gases—typical fluctuations,

    Tal Agranov, Sunghan Ro, Yariv Kafri, and Vivien Lecomte, “Exact fluctuating hydrodynamics of active lat- tice gases—typical fluctuations,” J. Stat. Mech. 2021, 083208 (2021)

    2021

  70. [78]

    En- tropy production and its large deviations in an active lattice gas,

    Tal Agranov, Michael E Cates, and Robert L Jack, “En- tropy production and its large deviations in an active lattice gas,” J. Stat. Mech. 2022, 123201 (2022)

    2022

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.