In this thesis, I use Doi-Peliti field theory to describe a range of active matter systems and calculate their entropy production.
The topics in this thesis are presented from the easier model to the more complicated model. In Chapter 2, I use the field theory to calculate the stationary density of a drift-diffusive particle in an external potential and compare the result with the well-known analytic solution. Here I show a basic route to study active matter via field theory, even though this process is already well studied. In Chapter 3, I show the propagator, mean-squared displacement and entropy production of run-and-tumble particles in d dimensions. In Chapter 4, I use field theory and introduce a corresponding eigensystem to obtain the propagator of active Brownian particles in 2 and 3 dimensions and calculate their entropy production. In Chapter 5, I extend our field theoretic framework to include interaction, calculate their correlation function and entropy production perturbatively, and compare the theory with numerical results.
Finally, in Chapter 6, I discuss the main results of this thesis and present the open
questions for further work.