This thesis aims to address problems in active matter by employing techniques in both stochastic processes and statistical field theories. It is mainly divided into two parts: first, applications of stochastic processes to find the entropy production of var- ious exactly solvable models and solve the dynamics of a Run-and-Tumble particle
in a piecewise linear potential, and second, applications of field theories to find the optimal shape for maximising currents of a Run-and-Tumble particle perturbatively and probing the particle identities using different field theories. In Chapter 1, I de- rive various methods and results from stochastic processes that are used in the rest
of the thesis. In Chapter 2, I present a self-contained review of entropy production and calculate it from first principles for various exactly solvable models. In Chap-
ter 3, I solve the steady-state dynamics of a Run-and-Tumble particle in a piece-
wise linear ratchet and calculate various other quantities such as particle current, entropy production and mean first passage time. In Chapter 4, I derive and present Doi-Peliti field theory and response field theory which are used in the rest of the the- sis. In Chapter 5, I present a method of solving the probability distribution perturba- tively and finding the optimal shape of the potential that maximises the probability current for a Run-and-Tumble particle using Doi-Peliti field theory. In Chapter 6, I identify the mechanism where particle entity is enforced in the context of the Doi- Peliti field theory of a diffusive particle and the response field theory that is derived from Dean’s equation.