Collective Behaviors in Active Matter

Equilibrium soft matter has transformed material sciences, from the usage of gels and foams in the health industry to that of liquid crystals in LCD screens. Our ability to tailor these materials stems from our understanding of their equilibrium steady-state behaviors: typical states are found by balancing energy and entropy. This guiding principle, however, limits the range of behaviors that can be observed: dynamical steady-states are forbidden and the Boltzmann factor limits the possible collective behaviors as much as it facilitates their study. Over the past twenty years, active materials have attracted an ever-growing interest: they comprise individual units that dissipate energy to exert mechanical forces on their environment and are hence driven strongly out of equilibrium. From the emergence of collective motion to that of low-Reynolds turbulent states, these materials have properties unmatched in passive systems. This rich phenomenology comes at the cost of losing the equilibrium toolbox, hence making the design of active materials a challenge.  In this colloquium, I will review standard active systems and discuss their atypical emerging properties. I will then illustrate the theoretical progress that has been made over the past decade to understand the large-scale physics of active materials, focusing in particular on the new phase transitions and mechanical properties that can be found in active matter.