Active matter refers to a class of systems that, at an individual particle level, can consume energy from their environments and convert it to mechanical work. Thus, the constituent entities of active matter, called active particles, are driven out of equilibrium. The intrinsic non-equilibrium nature of these particles is manifested in their dynamics, which breaks detailed balance, thus, making the problem of even a single active particle quite challenging. In this seminar, I will discuss some of our theoretical attempts to understand the effects of 'activity' on the spatiotemporal properties of non-interacting active particles and infer possible differences with their equilibrium counterparts. The talk will be broadly divided into the following parts:

(i) Introduction to active particles

(ii) Stochastic models of active particles and the fluctuations in the different physical observables

(ii) Effects of external forcing on the behavior of active particles

(iii) Energy transport in extended systems driven by active drive