Self-propelled particles include both self-phoretic synthetic colloids and various microorganisms. By continually consuming energy, they bypass the laws of equilibrium thermodynamics. These laws enforce the Boltzmann distribution in thermal equilibrium: The steady state is then independent of kinetic parameters. In contrast, self-propelled particles tend to accumulate where they move more slowly. They may also slow down at high density for either biochemical or steric reasons. This creates positive feedback, which can lead to motility-induced phase separation (MIPS) between dense and dilute fluid phases. At leading order in gradients, a mapping relates variable-speed, self-propelled particles to passive particles with attractions. This deep link to equilibrium phase separation is confirmed by simulations but generally breaks down at higher order in gradients: New effects, with no equilibrium counterpart, then emerge. We give a selective overview of the fast-developing field of MIPS, focusing on theory and simulation but including a brief speculative survey of its experimental implications.

Michael E. Cates

Julien Tailleur

Annual Review of Condensed Matter Physics

自 2010 年出版的凝聚态物理年度回顾描述了凝聚态物理和相关学科最重要的进展。该杂志通过确定最近的发展并提出对该领域各个部分的批判性评估，为正在进行的研究做出贡献。

The Annual Review of Condensed Matter Physics has been published since 2010 and aims to describe the significant advancements in condensed matter physics and related fields. The journal contributes to ongoing research by identifying recent developments and providing critical assessments of various aspects of the field.

《Annual Review of Condensed Matter Physics》自2010年起出版，旨在描述凝聚态物理及相关学科的重要进展。该杂志通过识别最新的发展，并对该领域的各个部分进行批判性评估，为持续的研究提供贡献。

Category	Quartile
物理与天体物理	1
物理与天体物理, 物理凝聚态物理	1

Motility-Induced Phase Separation

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Journal Info

Category	Quartile
PHYSICS, CONDENSED MATTER	1