中国物理B ›› 2025, Vol. 34 ›› Issue (9): 94702-094702.doi: 10.1088/1674-1056/ae030c

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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. 1 Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China;
    2 College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
  • 收稿日期:2025-08-13 修回日期:2025-08-27 接受日期:2025-09-04 出版日期:2025-08-21 发布日期:2025-09-04
  • 通讯作者: Joscha Mecke, Yongxiang Gao E-mail:joscha.mecke@szu.edu.cn;yongxiang.gao@szu.edu.cn
  • 基金资助:
    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).

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. 1 Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China;
    2 College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
  • Received:2025-08-13 Revised:2025-08-27 Accepted:2025-09-04 Online:2025-08-21 Published:2025-09-04
  • Contact: Joscha Mecke, Yongxiang Gao E-mail:joscha.mecke@szu.edu.cn;yongxiang.gao@szu.edu.cn
  • Supported by:
    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).

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摘要： 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.

关键词: active matter, active pressure, equation of state, active Brownian particles

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.

Key words: active matter, active pressure, equation of state, active Brownian particles

中图分类号:  (Electrokinetic effects)

  • 47.57.jd
05.70.Ln (Nonequilibrium and irreversible thermodynamics) 47.63.Gd (Swimming microorganisms) 05.70.Ce (Thermodynamic functions and equations of state)