|
|
|
Pressure in active matter |
| Guo Yu(余果)1, Ruiyao Li(李蕤耀)1, Fukang Li(李富康)1, Jiayu Zhang(张佳玉)1, Xiyue Li(李西月)1, Zequ Chen(陈泽渠)1, Joscha Mecke1,2,†, and Yongxiang Gao(高永祥)1,‡ |
1 Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China;
2 College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China |
|
|
|
|
Abstract In the last decade, the study of pressure in active matter has attracted growing attention due to its fundamental relevance to nonequilibrium statistical physics. Active matter systems are composed of particles that consume energy to sustain persistent motion, which are inherently far from equilibrium. These particles can exhibit complex behaviors, including motility-induced phase separation, clustering, and anomalous stress distributions, motivating the introduction of active swim stress and swim pressure. Unlike in passive fluids, pressure in active systems emerges from momentum flux originating from swim force rather than equilibrium conservative interactions, offering a distinct perspective for understanding their mechanical response. Simple models of active Brownian particles (ABPs) have been employed in theoretical and simulation studies across both dilute and dense regimes, revealing that pressure is a state function and exhibits a nontrivial dependence on density. Together with nonequilibrium statistical concepts such as effective temperature and effective adhesion, pressure offers important insight for understanding behaviors in active matter such as sedimentation equilibrium and motility induced phase separation. Extensions of ABP models beyond their simplest form have underscored the fragility of the pressure-based equation of state, which can break down under factors such as density-dependent velocity, torque, complex boundary geometries and interactions. Building on these developments, this review provides a comprehensive survey of theoretical and experimental advances, with particular emphasis on the microscopic origins of active pressure and the mechanisms underlying the breakdown of the equation of state.
|
Received: 13 August 2025
Revised: 27 August 2025
Accepted manuscript online: 04 September 2025
|
|
PACS:
|
47.57.jd
|
(Electrokinetic effects)
|
| |
05.70.Ln
|
(Nonequilibrium and irreversible thermodynamics)
|
| |
47.63.Gd
|
(Swimming microorganisms)
|
| |
05.70.Ce
|
(Thermodynamic functions and equations of state)
|
|
| Fund: Y.G. acknowledges financial support from the General Program of the National Natural Science Foundation of China (Grant No. 12474195), the Key Project of Guangdong Provincial Department of Education (Grant No. 2023ZDZX3021), and the Natural Science Foundation of Guangdong Province (Grant No. 2024A1515011343). |
Corresponding Authors:
Joscha Mecke, Yongxiang Gao
E-mail: joscha.mecke@szu.edu.cn;yongxiang.gao@szu.edu.cn
|
Cite this article:
Guo Yu(余果), Ruiyao Li(李蕤耀), Fukang Li(李富康), Jiayu Zhang(张佳玉), Xiyue Li(李西月), Zequ Chen(陈泽渠), Joscha Mecke, and Yongxiang Gao(高永祥) Pressure in active matter 2025 Chin. Phys. B 34 094702
|
[1] Ji F, Wu Y, Pumera M and Zhang L 2023 Adv. Mater. 35 2203959
[2] Illien P, Golestanian R and Sen A 2017 Chem. Soc. Rev. 46 5508
[3] Cavagna A and Giardina I 2014 Annual Review of Condensed Matter Physics 5 183
[4] Ramaswamy S 2010 Annual Review of Condensed Matter Physics 1 323
[5] Cates M E and Tailleur J 2015 Annual Review of Condensed Matter Physics 6 219
[6] Fruchart M, Hanai R, Littlewood P B and Vitelli V 2021 Nature 592 363
[7] Mallory S A, Valeriani C and Cacciuto A 2018 Annual Review of Physical Chemistry 69 59
[8] Huang Y, Wu C, Chen J and Tang J 2024 Angewandte Chemie 63 e202313885
[9] Yu N, Shah Z H, Yang M and Gao Y 2024 Research 7 0304
[10] Elgeti J, Winkler R G and Gompper G 2015 Reports on Progress in Physics 78 056601
[11] Mecke J, Nketsiah J O, Li R and Gao Y 2024 Natl. Sci. Open 3 20230086
[12] Bechinger C, Di Leonardo R, Löwen H, Reichhardt C, Volpe G and Volpe G 2016 Rev. Mod. Phys. 88 045006
[13] Dombrowski C, Cisneros L, Chatkaew S, Goldstein R E and Kessler J O 2004 Phys. Rev. Lett. 93 098103
[14] Kemkemer R, Kling D, Kaufmann D and Gruler H 2000 Euro. Phys. J. E 1 215
[15] Ballerini M, Cabibbo N, Candelier R, Cavagna A, Cisbani E, Giardina I, Lecomte V, Orlandi A, Parisi G, Procaccini A, Viale M and Zdravkovic V 2008 Proc. Natl. Acad. Sci. USA 105 1232
[16] Makris N C, Ratilal P, Jagannathan S, Gong Z, Andrews M, Bertsatos I, Godø O R, Nero R W and Jech J M 2009 Science 323 1734
[17] Marchetti M C, Joanny J F, Ramaswamy S, Liverpool T B, Prost J, Rao M and Simha R A 2013 Rev. Mod. Phys. 85 1143
[18] Partridge B L, Johansson J and Kalish J 1983 Environmental Biology of Fishes 9 253
[19] Vicsek T, Czirók A, Ben-Jacob E, Cohen I and Shochet O 1995 Phys. Rev. Lett. 75 1226
[20] Anderson C, Theraulaz G and Deneubourg J L 2002 Insectes Sociaux 49 99
[21] Gu F, Guiselin B, Bain N, Zuriguel I and Bartolo D 2025 Nature 638 112
[22] Ning L, Zhu H, Yang J, Zhang Q, Liu P, Ni R and Zheng N 2024 National Science Open 3 1
[23] Zhang J, Luijten E, Grzybowski B A and Granick S 2017 Chem. Soc. Rev. 46 5551
[24] Aditi Simha R and Ramaswamy S 2002 Phys. Rev. Lett. 89 058101
[25] Saintillan D and Shelley M J 2013 Comptes Rendus Physique 14 497
[26] Saintillan D and Shelley M J 2008 Phys. Rev. Lett. 100 178103
[27] Doostmohammadi A, Ignés-Mullol J, Yeomans J Mand Sagués F 2018 Nat. Commun. 9 3246
[28] Takatori S C, Yan W and Brady J F 2014 Phys. Rev. Lett. 113 028103
[29] Foss D R and Brady J F 2000 Journal of Rheology 44 629
[30] Mecke J, Gao Y, Ramírez Medina C A, Aarts D G A L, Gompper G and Ripoll M 2023 Communications Physics 6 324
[31] Bricard A, Caussin J B, Desreumaux N, Dauchot O and Bartolo D 2013 Nature 503 95
[32] Hall K R 1972 The Journal of Chemical Physics 57 2252
[33] Phan S E, Russel W B, Cheng Z, Zhu J, Chaikin P M, Dunsmuir J H and Ottewill R H 1996 Phys. Rev. E 54 6633
[34] Carnahan N F and Starling K E 1969 The Journal of Chemical Physics 51 635
[35] Solon A P, Fily Y, Baskaran A, Cates M E, Kafri Y, Kardar M and Tailleur J 2015 Nat. Phys. 11 673
[36] Mallory S A, Šarić A, Valeriani C and Cacciuto A 2014 Phys. Rev. E 89 052303
[37] Yang X, Manning M L and Marchetti M C 2014 Soft Matter 10 6477
[38] Ezhilan B, Alonso-Matilla R and Saintillan D 2015 Journal of Fluid Mechanics 781 R4
[39] Kaiser A, Wensink R and Löwen H 2012 Phys. Rev. Lett. 108 268307
[40] Jin K and Jing G Y 2019 Acta Phys. Sin. 68 170501 (in Chinese)
[41] Rands S 2011 Applied Animal Behaviour Science 134 83
[42] Takatori S and Brady J 2016 Current Opinion in Colloid & Interface Science 21 24
[43] Toner J, Tu Y and Ramaswamy S 2005 Annals of Physics 318 170
[44] Yu N, Shah Z H, Basharat M, Wang S, Zhou X, Lin G, Edwards S A, Yang M and Gao Y 2023 Soft Matter 19 9505
[45] Sokolov A, Apodaca M M, Grzybowski B A and Aranson I S 2010 Proc. Natl. Acad. Sci. USA 107 969
[46] Dushman S 1938 Journal of Chemical Education 15 550
[47] Quimby S L 1950 Science 112 95
[48] Brady J F 1993 The Journal of Chemical Physics 98 3335
[49] Reif F and Scott H L 1998 American Journal of Physics 66 164
[50] Landau L and Lifshitz E 2013 Fluid Mechanics: Landau and Lifshitz: Course of Theoretical Physics 1 1
[51] Truesdell C and Noll W 1965 The Non-Linear Field Theories of Mechanics, Flügge S ed. (Berlin: Springer) pp. 1-579
[52] Solon A P, Stenhammar J, Wittkowski R, Kardar M, Kafri Y, Cates M E and Tailleur J 2015 Phys. Rev. Lett. 114 198301
[53] Winkler R G, Wysocki A and Gompper G 2015 Soft Matter 11 6680
[54] Marini Bettolo Marconi U, Maggi C and Paoluzzi M 2017 The Journal of Chemical Physics 147 024903
[55] Ginot F, Theurkauff I, Detcheverry F, Ybert C and Cottin-Bizonne C 2018 Nat. Commun. 9 696
[56] Ginot F, Theurkauff I, Levis D, Ybert C, Bocquet L, Berthier L and Cottin-Bizonne C 2015 Phys. Rev. X 5 011004
[57] Speck T and Jack R L 2016 Phys. Rev. E 93 062605
[58] Romanczuk P, Bär M, Ebeling W, Lindner B and Schimansky-Geier L 2012 Eur. Phys. J. Spec. Top. 202 1
[59] Irving J H and Kirkwood J G 1950 The Journal of Chemical Physics 18 817
[60] Levis D, Codina J and Pagonabarraga I 2017 Soft Matter 13 8113
[61] Falasco G, Baldovin F, Kroy K and Baiesi M 2016 New J. Phys. 18 093043
[62] Cates M E and Tailleur J 2013 Europhys. Lett. 101 20010
[63] Doi M 2013 Soft Matter Physics 2 13
[64] Loi D, Mossa S and Cugliandolo L F 2008 Phys. Rev. E 77 051111
[65] Jamali T 2020 Active-Passive Brownian Particle in Two Dimensions
[66] Lindner B and Nicola E 2008 Euro. Phys. J. Spec. Top. 157 43
[67] Palacci J, Cottin-Bizonne C, Ybert C and Bocquet L 2010 Phys. Rev. Lett. 105 088304
[68] Baek Y, Solon A P, Xu X, Nikola N and Kafri Y 2018 Phys. Rev. Lett. 120 058002
[69] Takatori S C, De Dier R, Vermant J and Brady J F 2016 Nat. Commun. 7 10694
[70] Golestanian R, Liverpool T B and Ajdari A 2007 New J. Phys. 9 126
[71] Baxter R J 1968 The Journal of Chemical Physics 49 2770
[72] Post A J and Glandt E D 1986 The Journal of Chemical Physics 84 4585
[73] Caporusso C, Cugliandolo L, Digregorio P, Gonnella G and Suma A 2024 Soft Matter 20 4208
[74] Fily Y and Marchetti M C 2012 Phys. Rev. Lett. 108 235702
[75] Redner G S, Hagan M F and Baskaran A 2013 Phys. Rev. Lett. 110 055701
[76] Schnitzer M J 1993 Phys. Rev. E 48 2553
[77] Speck T, Bialké J, Menzel A and Löwen H 2013 Phys. Rev. Lett. 112 238301
[78] Tailleur J and Cates M E 2008 Phys. Rev. Lett. 100 218103
[79] Abaurrea Velasco C, Abkenar M, Gompper G and Auth T 2018 Phys. Rev. E 98 022605
[80] Bäuerle T, Fischer A, Speck T and Bechinger C 2018 Nat. Commun. 9 3232
[81] Fischer A, Schmid F and Speck T 2020 Phys. Rev. E 101 012601
[82] Ridgway W J M, Dalwadi M P, Pearce P and Chapman S J 2023 Phys. Rev. Lett. 131 228302
[83] Solon A P, Stenhammar J, CatesME, Kafri Y and Tailleur J 2018 Phys. Rev. E 97 020602
[84] Bialké J, Löwen H and Speck T 2013 Europhys. Lett. 103 30008
[85] Bialké J, Siebert J T, Löwen H and Speck 2015 Phys. Rev. Lett. 115 098301
[86] Caprini L and Marini Bettolo Marconi U 2021 The Journal of Chemical Physics 154 024902
[87] Takatori S C and Brady J F 2017 Phys. Rev. Fluids 2 094305
[88] Das S, Gompper G and Winkler R G 2019 Scientific Reports 9 6608
[89] Steffenoni S, Falasco G and Kroy K 2017 Phys. Rev. E 95 052142
[90] Joyeux M and Bertin E 2016 Phys. Rev. E 93 032605
[91] Pirhadi E, Cheng X and Yong X 2021 Scientific Reports 11 22204
[92] Lavergne F A, Wendehenne H, Bäuerle T and Bechinger C 2019 Science 364 70
[93] Caprini L and Marconi U 2018 Soft Matter 14 9044
[94] Fily Y, Baskaran A and Hagan M F 2014 Soft Matter 10 5609
[95] Nikola N, Solon A P, Kafri Y, Kardar M, Tailleur J and Voituriez R 2016 Phys. Rev. Lett. 117 098001
[96] Khatami M,Wolff K, Pohl O, EjtehadiMR and Stark H 2016 Scientific Reports 6 37670
[97] Fily Y, Baskaran A and Hagan M F 2015 Phys. Rev. E 91 012125
[98] Junot G, Briand G, Ledesma-Alonso R and Dauchot O 2017 Phys. Rev. Lett. 119 028002
[99] Yan W and Brady J F 2015 Soft Matter 11 6235
[100] Speck T 2020 Soft Matter 16 2652
[101] Sun Z, Li L, Wang C, Wang J, Chen H, Wang G, Liu L, Ye F and Yang M 2025 Intrinsic pressure as a convenient mechanical framework for dry active matter
[102] Banerjee D, Souslov A, Abanov A G and Vitelli V 2017 Nat. Commun. 8 1573
[103] Mecke J, Gao Y, Ramírez Medina C A, Aarts D G A L, Gompper G and Ripoll M 2023 Commun. Phys. 6 324
[104] Fodor ′E and Cates M E 2021 Europhys. Lett. 134 10003 |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
