The principle of least action is a fundamental principle in physics that states that the laws of motion can be derived from a single quantity called the action, which is minimized along the actual path taken by a physical system. The action is defined as the integral of a [[Lagrangian]] function over time, which describes the system's dynamics. It takes into account the system's position, velocity, and potential energy. The Lagrangian function represents the [[Subtraction|difference]] between kinetic energy and potential energy and determines how the system evolves over time. According to the principle of least action, when a physical system moves from one state to another, it follows a path that minimizes the action. This means that out of all possible paths connecting these two states, nature chooses the one with the lowest action. This path is known as the "path of least action" or "the path of stationary action." The principle of least action has profound implications in classical mechanics and other areas of physics. It provides an alternative formulation to Newton's laws of motion and allows for a more elegant and concise description of physical phenomena. It is also closely related to Hamilton's principle in classical mechanics and Fermat's principle in optics. Furthermore, this principle has been extended to other branches of physics like quantum mechanics, where it serves as a foundation for understanding particle behavior at microscopic scales. In quantum field theory, for example, particles are described as excitations in fields that minimize their respective actions. Overall, the principle of least action provides a powerful mathematical tool for understanding and predicting the behavior of physical systems across various domains in physics.