Sommaire:

Flocks of birds, bacteria colonies, sheep herds, crowds of people ... are just some common examples of large groups of living entities behaving in a remarkable collective fashion. From a physicists viewpoint, these are systems composed of many interacting units, each somehow able to convert energy from their environment to stay 'alive' and perform some task. Such dynamics lifts the constraints imposed by equilibrium, opening many challenges and eventually the possibility for the rich phenomena displayed in the natural world. However, we lack a general theoretical framework to describe it. Much understanding has been gained from the investigation of model systems (both theoretical and experimental), usually dealing with 'active units' consisting in self-propelled particles with simple physical interactions, such as excluded volume. Interestingly, the mere competition between self-propulsion and crowding, is already enough to trigger a novel non-equilibrium phase transition. I will review our current understanding of this phenomenon, and I will then delve into a complementary perspective on active systems, as made of entities that interact in a non-reciprocal way. This will lead us to consider 'active' extensions of paradigmatic models in statistical mechanics, such as the Ising model, to decipher what such new ingredient brings into the classical picture of phase transitions.

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