Phase space is a mathematical concept used in physics and engineering to represent all possible states of a system. Each state is defined by a set of variables, such as position and momentum, which are plotted in a multi-dimensional space. For example, in a simple system, one axis might represent position while another represents velocity, allowing for a complete visualization of the system's behavior. In phase space, trajectories show how a system evolves over time. These paths can reveal important information about stability and dynamics. Understanding phase space is crucial in fields like classical mechanics, thermodynamics, and quantum mechanics, as it helps predict how systems will respond to different conditions.