- Letter
- Open Access
Mechanical inhibition of dissipation in a thermodynamically consistent active solid
Phys. Rev. Research 7, L042062 – Published 16 December, 2025
DOI: https://doi.org/10.1103/tgyv-5vqv
Abstract
The study of active solids offers a window into the mechanics and thermodynamics of dense living matter. A key aspect of the nonequilibrium dynamics of such active systems is a mechanistic description of how the underlying mechanochemical couplings arise, which cannot be resolved in models that are phenomenologically constructed. Here, we follow a bottom-up theoretical approach to develop a thermodynamically consistent active solid model and uncover a nontrivial crosstalk that naturally ensues between mechanical response and dissipation. In particular, we show that dissipation reaches a maximum at finite stresses, while it is inhibited under large stresses, effectively reverting the system to a passive state. Our findings establish a generic mechanism plausibly responsible for the nonmonotonic behavior observed in recent experimental measurements of entropy production rate in an actomyosin material and enzymatic activity in crowded condensates.
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References (100)
- J. Prost, F. Jülicher, and J.-F. Joanny, Active gel physics, Nat. Phys. 11, 111 (2015).
- G. H. Koenderink, Z. Dogic, F. Nakamura, P. M. Bendix, F. C. MacKintosh, J. H. Hartwig, T. P. Stossel, and D. A. Weitz, An active biopolymer network controlled by molecular motors, Proc. Natl. Acad. Sci. USA 106, 15192 (2009).
- T. Strübing, A. Khosravanizadeh, A. Vilfan, E. Bodenschatz, R. Golestanian, and I. Guido, Wrinkling instability in 3D active nematics, Nano Lett. 20, 6281 (2020).
- D. Bi, J. H. Lopez, J. M. Schwarz, and M. L. Manning, A density-independent rigidity transition in biological tissues, Nat. Phys. 11, 1074 (2015).
- S. Garcia, E. Hannezo, J. Elgeti, J.-F. Joanny, P. Silberzan, and N. S. Gov, Physics of active jamming during collective cellular motion in a monolayer, Proc. Natl. Acad. Sci. USA 112, 15314 (2015).
- D. Bi, X. Yang, M. C. Marchetti, and M. L. Manning, Motility-driven glass and jamming transitions in biological tissues, Phys. Rev. X 6, 021011 (2016).
- R. Alert and X. Trepat, Physical models of collective cell migration, Annu. Rev. Condens. Matter Phys. 11, 77 (2020).
- J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, Living crystals of light-activated colloidal surfers, Science 339, 936 (2013).
- I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, and T. Speck, Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles, Phys. Rev. Lett. 110, 238301 (2013).
- H. Massana-Cid, F. Meng, D. Matsunaga, R. Golestanian, and P. Tierno, Tunable self-healing of magnetically propelling colloidal carpets, Nat. Commun. 10, 2444 (2019).
- H. Shen, P. Tan, and L. Xu, Probing the role of mobility in the collective motion of nonequilibrium systems, Phys. Rev. Lett. 116, 048302 (2016).
- P. Baconnier, D. Shohat, C. H. López, C. Coulais, V. Démery, G. Düring, and O. Dauchot, Selective and collective actuation in active solids, Nat. Phys. 18, 1234 (2022).
- C. Hernández-López, P. Baconnier, C. Coulais, O. Dauchot, and G. Düring, Model of active solids: Rigid body motion and shape-changing mechanisms, Phys. Rev. Lett. 132, 238303 (2024).
- J. Veenstra, C. Scheibner, M. Brandenbourger, J. Binysh, A. Souslov, V. Vitelli, and C. Coulais, Adaptive locomotion of active solids, Nature (London) 639, 935 (2025).
- N. Uchida and R. Golestanian, Synchronization and collective dynamics in a carpet of microfluidic rotors, Phys. Rev. Lett. 104, 178103 (2010).
- N. Oppenheimer, D. B. Stein, and M. J. Shelley, Rotating membrane inclusions crystallize through hydrodynamic and steric interactions, Phys. Rev. Lett. 123, 148101 (2019).
- T. H. Tan, A. Mietke, J. Li, Y. Chen, H. Higinbotham, P. J. Foster, S. Gokhale, J. Dunkel, and N. Fakhri, Odd dynamics of living chiral crystals, Nature (London) 607, 287 (2022).
- R. Golestanian, Collective behavior of thermally active colloids, Phys. Rev. Lett. 108, 038303 (2012).
- J. Agudo-Canalejo and R. Golestanian, Active phase separation in mixtures of chemically interacting particles, Phys. Rev. Lett. 123, 018101 (2019).
- K. R. Prathyusha, S. Saha, and R. Golestanian, Anomalous fluctuations in a droplet of chemically active colloids or enzymes, Phys. Rev. Lett. 133, 058401 (2024).
- M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
- Y. Fily and M. C. Marchetti, Athermal phase separation of self-propelled particles with no alignment, Phys. Rev. Lett. 108, 235702 (2012).
- P. Digregorio, D. Levis, A. Suma, L. F. Cugliandolo, G. Gonnella, and I. Pagonabarraga, Full phase diagram of active Brownian disks: From melting to motility-induced phase separation, Phys. Rev. Lett. 121, 098003 (2018).
- B. M. Mognetti, A. Šarić, S. Angioletti-Uberti, A. Cacciuto, C. Valeriani, and D. Frenkel, Living clusters and crystals from low-density suspensions of active colloids, Phys. Rev. Lett. 111, 245702 (2013).
- L. Caprini, U. Marini Bettolo Marconi, A. Puglisi, and H. Löwen, Entropons as collective excitations in active solids, J. Chem. Phys. 159, 041102 (2023).
- L. Caprini, U. M. B. Marconi, and H. Löwen, Entropy production and collective excitations of crystals out of equilibrium: The concept of entropons, Phys. Rev. E 108, 044603 (2023).
- G. Briand, M. Schindler, and O. Dauchot, Spontaneously flowing crystal of self-propelled particles, Phys. Rev. Lett. 120, 208001 (2018).
- J. Deseigne, O. Dauchot, and H. Chaté, Collective motion of vibrated polar disks, Phys. Rev. Lett. 105, 098001 (2010).
- H. Xu, Y. Huang, R. Zhang, and Y. Wu, Autonomous waves and global motion modes in living active solids, Nat. Phys. 19, 46 (2023).
- R. Dreyfus, J. Baudry, M. L. Roper, M. Fermigier, H. A. Stone, and J. Bibette, Microscopic artificial swimmers, Nature (London) 437, 862 (2005).
- R. G. Winkler and G. Gompper, The physics of active polymers and filaments, J. Chem. Phys. 153, 040901 (2020).
- V. Bianco, E. Locatelli, and P. Malgaretti, Globulelike conformation and enhanced diffusion of active polymers, Phys. Rev. Lett. 121, 217802 (2018).
- E. Locatelli, V. Bianco, and P. Malgaretti, Activity-induced collapse and arrest of active polymer rings, Phys. Rev. Lett. 126, 097801 (2021).
- S. K. Anand and S. P. Singh, Structure and dynamics of a self-propelled semiflexible filament, Phys. Rev. E 98, 042501 (2018).
- K. R. Prathyusha, F. Ziebert, and R. Golestanian, Emergent conformational properties of end-tailored transversely propelling polymers, Soft Matter 18, 2928 (2022).
- E. M. Purcell, Life at low Reynolds number, Am. J. Phys. 45, 3 (1977).
- A. Najafi and R. Golestanian, Simple swimmer at low Reynolds number: Three linked spheres, Phys. Rev. E 69, 062901 (2004).
- R. Golestanian, T. B. Liverpool, and A. Ajdari, Propulsion of a molecular machine by asymmetric distribution of reaction products, Phys. Rev. Lett. 94, 220801 (2005).
- R. Golestanian and A. Ajdari, Analytic results for the three-sphere swimmer at low Reynolds number, Phys. Rev. E 77, 036308 (2008).
- E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Rep. Prog. Phys. 72, 096601 (2009).
- To give but one example, consider the fact that the zero self-propulsion speed limit of hard-core particles with Vicsek-type alignment interactions is in fact not an equilibrium one [96].
- A. Daddi-Moussa-Ider, R. Golestanian, and A. Vilfan, Minimum entropy production by microswimmers with internal dissipation, Nat. Commun. 14, 6060 (2023).
- R. Golestanian, Hydrodynamically consistent many-body Harada-Sasa relation, Phys. Rev. Lett. 134, 207101 (2025).
- J. H. Fritz and U. Seifert, Thermodynamically consistent model of an active Ornstein–Uhlenbeck particle, J. Stat. Mech. (2023) 093204.
- M. Chatzittofi, J. Agudo-Canalejo, and R. Golestanian, Entropy production and thermodynamic inference for stochastic microswimmers, Phys. Rev. Res. 6, L022044 (2024).
- T. Agranov, R. L. Jack, M. E. Cates, and É. Fodor, Thermodynamically consistent flocking: From discontinuous to continuous transitions, New J. Phys. 26, 063006 (2024).
- R. Bebon, J. F. Robinson, and T. Speck, Thermodynamics of active matter: Tracking dissipation across scales, Phys. Rev. X 15, 021050 (2025).
- K. Proesmans, G. Falasco, A. T. Mohite, M. Esposito, and É. Fodor, Quantifying dissipation in flocking dynamics: When tracking internal states matters, Phys. Rev. E 112, 024103 (2025).
- T. Agranov, R. L. Jack, M. E. Cates, and É. Fodor, Entropy production rate in thermodynamically consistent flocks, New J. Phys. 27 104602 (2025).
- M. Chatzittofi, J. Agudo-Canalejo, and R. Golestanian, Mechanistic rules for de novo design of enzymes, Chem. Catal. 5, 101394 (2025).
- M. O. Magnasco, Molecular combustion motors, Phys. Rev. Lett. 72, 2656 (1994).
- K. J. Challis and M. W. Jack, Energy transfer in a molecular motor in the Kramers regime, Phys. Rev. E 88, 042114 (2013).
- D. Keller and C. Bustamante, The mechanochemistry of molecular motors, Biophys. J. 78, 541 (2000).
- N. Golubeva, A. Imparato, and L. Peliti, Efficiency of molecular machines with continuous phase space, Europhys. Lett. 97, 60005 (2012).
- M. W. Jack, N. J. López-Alamilla, and K. J. Challis, Thermodynamic uncertainty relations and molecular-scale energy conversion, Phys. Rev. E 101, 062123 (2020).
- S. Garcia-Manyes and A. E. Beedle, Steering chemical reactions with force, Nat. Rev. Chem. 1, 0083 (2017).
- S. Liepelt and R. Lipowsky, Kinesin's network of chemomechanical motor cycles, Phys. Rev. Lett. 98, 258102 (2007).
- R. Golestanian and A. Ajdari, Mechanical response of a small swimmer driven by conformational transitions, Phys. Rev. Lett. 100, 038101 (2008).
- M. Chatzittofi, J. Agudo-Canalejo, and R. Golestanian, Nonlinear response theory of molecular machines, Europhys. Lett. 147, 21002 (2024).
- P. Baerts, U. Basu, C. Maes, and S. Safaverdi, Frenetic origin of negative differential response, Phys. Rev. E 88, 052109 (2013).
- A. Sarracino, F. Cecconi, A. Puglisi, and A. Vulpiani, Nonlinear response of inertial tracers in steady laminar flows: Differential and absolute negative mobility, Phys. Rev. Lett. 117, 174501 (2016).
- P. Rizkallah, A. Sarracino, O. Bénichou, and P. Illien, Absolute negative mobility of an active tracer in a crowded environment, Phys. Rev. Lett. 130, 218201 (2023).
- C. Nardini, E. Fodor, E. Tjhung, F. van Wijland, J. Tailleur, and M. E. Cates, Entropy production in field theories without time-reversal symmetry: Quantifying the non-equilibrium character of active matter, Phys. Rev. X 7, 021007 (2017).
- S. Ro, B. Guo, A. Shih, T. V. Phan, R. H. Austin, D. Levine, P. M. Chaikin, and S. Martiniani, Model-free measurement of local entropy production and extractable work in active matter, Phys. Rev. Lett. 129, 220601 (2022).
- T. Markovich, E. Fodor, E. Tjhung, and M. E. Cates, Thermodynamics of active field theories: Energetic cost of coupling to reservoirs, Phys. Rev. X 11, 021057 (2021).
- D. S. Seara, V. Yadav, I. Linsmeier, A. P. Tabatabai, P. W. Oakes, S. M. A. Tabei, S. Banerjee, and M. P. Murrell, Entropy production rate is maximized in non-contractile actomyosin, Nat. Commun. 9, 4948 (2018).
- S. Chen, D. S. Seara, A. Michaud, S. Kim, W. M. Bement, and M. P. Murrell, Energy partitioning in the cell cortex, Nat. Phys. 20, 1824 (2024).
- I. F. Davidson, B. Bauer, D. Goetz, W. Tang, G. Wutz, and J.-M. Peters, DNA loop extrusion by human cohesin, Science 366, 1338 (2019).
- P. Illien, T. Adeleke-Larodo, and R. Golestanian, Diffusion of an enzyme: The role of fluctuation-induced hydrodynamic coupling, Europhys. Lett. 119, 40002 (2017).
- J. Agudo-Canalejo, T. Adeleke-Larodo, P. Illien, and R. Golestanian, Synchronization and enhanced catalysis of mechanically coupled enzymes, Phys. Rev. Lett. 127, 208103 (2021).
- M. Chatzittofi, R. Golestanian, and J. Agudo-Canalejo, Topological phase locking in stochastic oscillators, Nat. Commun. 16, 4835 (2025).
- D. J. Bonthuis and R. Golestanian, Mechanosensitive channel activation by diffusio-osmotic force, Phys. Rev. Lett. 113, 148101 (2014).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/tgyv-5vqv for further details on mathematical derivations and numerical methods, as well as additional findings not included in the main text, which also includes Refs. [97, 98, 99].
- Z. Tang, J. Wu, S. Wu, W. Tang, J.-R. Zhang, W. Zhu, J.-J. Zhu, and Z. Chen, Single molecule–driven nanomotors reveal the dynamic-disordered chemomechanical transduction of active enzymes, Sci. Adv. 11, eads0446 (2025).
- M. Centola, E. Poppleton, S. Ray, M. Centola, R. Welty, J. Valero, N. G. Walter, P. Šulc, and M. Famulok, A rhythmically pulsing leaf-spring DNA-origami nanoengine that drives a passive follower, Nat. Nanotechnol. 19, 226 (2024).
- R. Golestanian, Synthetic mechanochemical molecular swimmer, Phys. Rev. Lett. 105, 018103 (2010).
- L. Cocconi, R. Garcia-Millan, Z. Zhen, B. Buturca, and G. Pruessner, Entropy production in exactly solvable systems, Entropy 22, 1252 (2020).
- C. Maes, Local detailed balance, SciPost Phys. Lect. Notes 32 (2021).
- P. Reimann, C. Van den Broeck, H. Linke, P. Hänggi, J. M. Rubi, and A. Pérez-Madrid, Giant acceleration of free diffusion by use of tilted periodic potentials, Phys. Rev. Lett. 87, 010602 (2001).
- G. Pavliotis and A. Stuart, Multiscale Methods: Averaging and Homogenization (Springer Science & Business Media, New York, NY, 2008).
- U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
- J. Schnakenberg, Network theory of microscopic and macroscopic behavior of master equation systems, Rev. Mod. Phys. 48, 571 (1976).
- The possibility to clearly identify the nonequilibrium cycles in a complex state space is another advantage of explicitly enforcing LDB. Phenomenological active models coupling discrete and continuous degrees of freedom may often result in an infinity of cycles of nonvanishing affinity, in which case calculating requires knowledge of the full probability current density.
- J. D. Weeks, D. Chandler, and H. C. Andersen, Role of repulsive forces in determining the equilibrium structure of simple liquids, J. Chem. Phys. 54, 5237 (1971).
- J. Moller and R. P. Waagepetersen, Statistical Inference and Simulation for Spatial Point Processes (Chapman and Hall/CRC, New York, NY, 2003).
- E. Zeeman, Stability of dynamical systems, Nonlinearity 1, 115 (1988).
- W. Huang, M. Ji, Z. Liu, and Y. Yi, Steady states of Fokker–Planck equations: I. Existence, J. Dyn. Differ. Equations 27, 721 (2015).
- D. Frydel, Entropy production of active particles formulated for underdamped dynamics, Phys. Rev. E 107, 014604 (2023).
- M. Dindo, J. Metson, W. Ren, M. Chatzittofi, K. Yagi, Y. Sugita, R. Golestanian, and P. Laurino, Enzymes can activate and mobilize the cytoplasmic environment across scales, bioRxiv, https://doi.org/10.1101/2025.01.28.635259.
- I. D. Terlizzi, M. Gironella, D. Herraez-Aguilar, T. Betz, F. Monroy, M. Baiesi, and F. Ritort, Variance sum rule for entropy production, Science 383, 971 (2024),.
- C. P. Brangwynne, C. R. Eckmann, D. S. Courson, A. Rybarska, C. Hoege, J. Gharakhani, F. Jülicher, and A. A. Hyman, Germline P granules are liquid droplets that localize by controlled dissolution/condensation, Science 324, 1729 (2009).
- E. Sokolova, E. Spruijt, M. M. K. Hansen, E. Dubuc, J. Groen, V. Chokkalingam, A. Piruska, H. A. Heus, and W. T. S. Huck, Enhanced transcription rates in membrane-free protocells formed by coacervation of cell lysate, Proc. Natl. Acad. Sci. USA 110, 11692 (2013).
- A. A. Hyman, C. A. Weber, and F. Jülicher, Liquid-liquid phase separation in biology, Annu. Rev. Cell Dev. Biol. 30, 39 (2014).
- D. Zwicker, R. Seyboldt, C. A. Weber, A. A. Hyman, and F. Jülicher, Growth and division of active droplets provides a model for protocells, Nat. Phys. 13, 408 (2017).
- E. S. Haswell, R. Phillips, and D. C. Rees, Mechanosensitive channels: What can they do and how do they do it? Structure 19, 1356 (2011).
- H. Tasaki, Hohenberg-Mermin-Wagner-type theorems for equilibrium models of flocking, Phys. Rev. Lett. 125, 220601 (2020).
- A. W. C. Lau and T. C. Lubensky, State-dependent diffusion: Thermodynamic consistency and its path integral formulation, Phys. Rev. E 76, 011123 (2007).
- A. Kobayashi, K. Yasuda, L.-S. Lin, I. Sou, Y. Hosaka, and S. Komura, Simulations of odd microswimmers, J. Phys. Soc. Jpn. 92, 034803 (2023).
- C. Benoit, Note sur une méthode de résolution des équations normales provenant de l'application de la méthode des moindres carrés a un système d'équations linéaires en nombre inférieur a celui des inconnues. — Application de la méthode a la résolution d'un système defini d'équations linéaires, Bull. Géod. 2, 67 (1924).
- L. Cocconi, M. Chatzittofi, and R. Golestanian, Mechanical inhibition of dissipation in a thermodynamically consistent active solid [Data set], Zenodo (2025), doi: 10.5281/zenodo.17801940.