Stochastic Differential Equations in Physics

Stochastic Differential Equations (SDEs) are powerful mathematical tools used to model systems subject to random fluctuations. In physics, SDEs find widespread applications ranging from statistical mechanics to quantum field theory. This paper provides an in-depth exploration of the theoretical foundations of SDEs in physics, their applications, and their implications in understanding complex physical phenomena. We delve into the mathematical framework of SDEs, their numerical solutions, and their role in modeling various physical processes. Furthermore, we present case studies illustrating the practical relevance of SDEs in different branches of physics.