Fluctuations in Active Fluids

Active fluids are typical nonequilibrium systems and exhibit anomalous density fluctuations, or long-range density correlations, that are absent in equilibrium fluids. In this chapter, we review several types of anomalous density fluctuations observed in active fluids. In polar active fluids, active nematics, and systems of self-propelled rods, one observes enhanced density fluctuations known as giant number fluctuations (GNF). We first introduce GNF and provide a qualitative description of this phenomenon using continuum models of active fluids. We then discuss density fluctuations in two-dimensional chiral active fluids. While active fluids typically exhibit GNF, chiral active fluids instead show a suppression of density fluctuations, a phenomenon known as hyperuniformity. Finally, we discuss density fluctuations in active fluids with spatial anisotropy, which are known to exhibit singular behavior in their density correlation functions.