Dynamical and thermodynamical origins of motility-induced phase separation

Active matter systems are inherently out of equilibrium and break the detailed balance (DB) at the microscopic scale, exhibiting vital collective phenomena such as motility -induced phase separation (MIPS). Here, we introduce a coarse -grained mapping method to probe DB breaking in the density -energy phase space, which allows us to reveal the dynamical and thermodynamical origins of MIPS based on the landscape -flux theory. Hallmarks of nonequilibrium properties are manifested by identifying the visible steady-state probability flux in the coarse -grained phase space. Remarkably, the flux of the system with activity lower than the MIPS threshold has the tendency to split the single potential well of the uniformdensity phase and generate two wells of phases with different densities, demonstrating that the nonequilibrium flux is the dynamical origin of MIPS. Moreover, we find that the entropy production rate shows a transition of scaling behavior around the MIPS threshold, providing an indicator for the thermodynamical origin of MIPS.