Fluctuations in Equilibrium Fluids

The main focus of this thesis is on fluctuations in active matter. To highlight their anomalous nature, it is instructive to first review fluctuations in equilibrium fluids before turning to the case of active matter. We begin by introducing the density correlation function, known as the structure factor, which is one of the central quantities studied in this thesis. We then discuss the dynamics of density fluctuations in an equilibrium fluid composed of colloidal particles. The dynamical equation governing density fluctuations is derived from the overdamped Langevin equation, and the structure factor is subsequently calculated from this equation. The calculation procedure presented here will also be applied to active systems.