Self-propelled particles are microscopic entities of typical size smaller than 1 micrometer (1/100 of the thickness of a human hair) that exhibit persistent random motion in a medium such as oil or water, due to a continuous intake of energy from its surroundings. Such physical systems are also labelled as active matter. A microorganism, such as a bacterium, is a perfect example of active matter found in nature. Other synthetic examples comprise of Janus (two-faced) particles which can move in a chemical solution when illuminated by light. A large collection of these constituents (or agents) shows extremely interesting phenomena like clustering, condensation and phase separation which otherwise are not observable for ‘passive’ systems and are highly desirable technologically in applications involving drug delivery, cleaning pollutants from water, oil recovery etc.
The out-of-equilibrium nature of these systems makes it difficult to predict their behaviour since the known equilibrium physics does not apply directly to such systems. Hence, there is a significant research devoted to exploring an extended thermodynamical description of these systems. In this thesis, we study the collective behaviour of such systems using a simple model, called as the active Brownian particle model, and the tools of statistical physics and computer simulations. We explore some of the principles which govern their emergent behaviour such as phase separation and the effects at the interface. We systematically investigate how does an increasing drive/activity pushes the system away from equilibrium and how certain known physical quantities can be extended to account for these effects.