Osmosis is a universal phenomenon occurring in a broad variety of processes and fields. It
is the archetype of entropic forces, both trivial in its fundamental expression–the van't Hoff …

Differently from passive Brownian particles, active particles, also known as self-propelled
Brownian particles or microswimmers and nanoswimmers, are capable of taking up energy …

Active matter systems are driven out of thermal equilibrium by a lack of generalized Stokes-
Einstein relation between injection and dissipation of energy at the microscopic scale. We …

Active colloids are microscopic particles, which self-propel through viscous fluids by
converting energy extracted from their environment into directed motion. We first explain …

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 …

Pressure is the mechanical force per unit area that a confined system exerts on its container.
In thermal equilibrium, it depends only on bulk properties—such as density and temperature …

Active matter encompasses systems whose individual constituents dissipate energy to exert
propelling forces on their environment. These systems exhibit dynamical phenomena with …

We derive a microscopic expression for the mechanical pressure P in a system of spherical
active Brownian particles at density ρ. Our exact result relates P, defined as the force per unit …

Active-matter systems operate far from equilibrium because of the continuous energy
injection at the scale of constituent particles. At larger scales, described by coarse-grained …

Many microorganisms, with phytoplankton and zooplankton as prominent examples, display
phototactic behaviour, that is, the ability to perform directed motion within a light gradient …