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Motility-induced phase separation (MIPS) leads to cohesive active matter in the absence of cohesive forces. We present, extend and illustrate a recent generalized thermodynamic formalism which accounts for its binodal curve. Using this formalism, we identify both a generalized surface tension, that controls finite-size corrections to coexisting densities, and generalized forces, that can be used to construct new thermodynamic ensembles. Our framework is based on a nonequilibrium generalization of the Cahn-Hilliard equation and we discuss its application to active particles interacting either via quorum-sensing interactions or directly through pairwise forces.
We establish the complete phase diagram of self-propelled hard disks in two spatial dimensions from the analysis of the equation of state and the statistics of local order parameters. The equilibrium melting scenario is maintained at small activities
Active Brownian particles (ABPs, such as self-phoretic colloids) swim at fixed speed $v$ along a body-axis ${bf u}$ that rotates by slow angular diffusion. Run-and-tumble particles (RTPs, such as motile bacteria) swim with constant $u$ until a random
A collection of self-propelled particles with volume exclusion interactions can exhibit the phenomenology of gas-liquid phase separation, known as motility-induced phase separation (MIPS). The non-equilibrium nature of the system is fundamental to th
We review understanding of kinetics of fluid phase separation in various space dimensions. Morphological differences, percolating or disconnected, based on overall composition in a binary liquid or density in a vapor-liquid system, have been pointed
Using computer simulations and dynamic mean-field theory, we demonstrate that fast enough rotation of circle active Brownian particles in two dimensions generates a dynamical clustering state interrupting the conventional motility induced phase separ