An introduction to the statistical physics of active matter: motility-induced phase separation and the “generic instability” of active gels

In this work we review some statistical physics techniques to coarse grain active matter systems, writing down a set of continuum fields which track the evolution of macroscopic fields such as density, momentum, etc. While the method can be applied in general, we will focus here on two simple and by now well-studied, active matter examples. First, we will consider motility-induced phase separation, the phenomenon by which a concentrated suspension of self-propelled particles spontaneously separates into a dense and a dilute phase. Second, we will review the so-called “generic instability” of active gels, which refers to the nonequilibrium phase transition between a quiescent and a spontaneously flowing phase in a concentrated suspension of rodlike active particles. For both these cases, we also outline recent developments in the literature.