Active matter and collective behaviour

Printemps- Eté
Niveau Master 2 3 ECTS - En anglais
Enseignant(s) Carine DOUARCHE ( Université Paris-Saclay ) Charlie DUCLUT ( Sorbonne Université I. Curie )
Contact - Secrétariat de l’enseignement

Tél : + 33 (1) 44 32 35 60

Contact - Secrétariat pédagogique

Tel : + 33 (1) 44 32 35 60 
Médina Mahrez 


Sorbonne Université

Université Paris Cité

Université Paris-Saclay 

Institut Polytechnique de Paris

Ecole Normale Supérieure

The lectures offer a statistical-physics perspective on active matter, which encompasses systems whose fundamental constituents dissipate energy to exert forces on the environment. This out-of-equilibrium microscopic drive endows active systems with properties unmatched in passive ones. From molecular motors to bacteria and animals, active agents are found at all scales in nature. Over the past twenty years, physicists and chemists have also engineered synthetic active systems in the lab, by motorizing particles whose sizes range from nanometers to centimeters, hence paving the way towards the engineering of active materials.

The lectures will rely on the modern tools of statistical mechanics, from stochastic calculus to field theoretical methods, using both theoretical models and experimental systems to illustrate the rich physics of active matter.

  • Active matter at microscopic scales 
    • Models of active particles; dynamics; non-Boltzmann statistics
  • Collective behavior of active particles
    • Motility-induced phase separation; from micro to macro
  • Large-scale (hydrodynamic) description of active matter
    • Irreversible thermodynamics of active matter; active polar gels
  • equilibrium statistical mechanics
  • stochastic calculus

Written exam


Gardiner, Handbook of stochastic methods for physics, chemistry and the natural sciences, Springer (1995)

Marchetti, et al., Hydrodynamics of soft active matter, Rev. Mod. Phys. 85, 1143 (2013)

K. Sekimoto, Stochastic Energetics, Springer (2010)

Van Kampen, Stochastic processes in Physics and Chemistry, Elsevier (1992)