Statistical Mechanics of Self-Propelled Systems

This thesis aims to unveil the statistical properties of self-propelled microswimmers, a non-equilibrium system in the variegate field of active matter. We shall employ stochastic and hydrodynamics approaches to explain the non-equilbrium behavior of self-propelled entities. We begin by studying suspensions of dilute active particles also in the presence of chirality. The dynamics in the presence of confinement traps is numerically and theoretically investigated employing effective equilibrium theories or effective equations for the moments of the distribution. As far as, the energetics properties of self-propelled particles are unveiled employing stochastic thermodynamic approaches. Besides, the experimental phenomenology of the accumulation near the walls is reviewed and original contributions to its theoretical understanding are developed, employing suitable hydrodynamic approaches and detecting their transport properties. Collective fascinating phenomena displayed by self-propelled unities are reviewed and numerically investigated, featuring new long-range orders in the velocity orientations which were not unveiled, up to now. In particular, the non-equilibrium aggregation phases of Active Matter reveal intriguing new features in the presence of an effective alignment interaction induced by the interplay between self-propulsion and excluded volume effects. Even the dilute phase shows the formation of bond (but unstable) pairs, while for denser suspensions of particles a continuous transition with aligned or vortex-like domains coexists with clustering and motility induced phase separation. The usual scenario of equilibrium aggregation phases is strongly modified even at the denser regimes, where the occurrence of empty moving regions or traveling crystals does not have a passive Brownian counterpart.