Potential Energy

physics

Definition

Potential Energy

Potential energy is the form of energy stored in the configuration of a physical system. It is a function $U(\mathbf{x})$ of the system’s position in configuration space, such that the force derived from it is

$$\mathbf{F}=-\nabla U.$$

The minus sign encodes that the force points towards decreasing potential: the system accelerates in the direction that lowers its stored energy. Because only differences $\Delta U$ produce observable forces, $U$ is defined up to an additive constant.