Evolution (physics)

Evolution is the change of a physical system’s state over time under its governing laws. Its description may be deterministic or probabilistic, depending on the theory and the system.

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Equation of motion: A mathematical relation that specifies how a physical system changes with time. Equations of motion encode the laws that generate a system’s trajectory.
Physical state: A specification of the properties of a physical system relevant to a theory. Evolution is defined as change in the system’s state.
Time-reversal symmetry: A symmetry under reversing the direction of time and transforming the system appropriately. Time-reversal symmetry concerns whether reversed histories obey the same laws, not merely forward evolution.
Dynamical system: A system whose state changes over time according to a specified rule or law. Physical evolution is a central instance of dynamical-system behavior.
Initial-value problem: A problem that determines a system’s future from its governing equations and state at an initial time. Evolution is predicted by supplying an initial state to the dynamical laws.
State space: The set of possible states of a system, represented mathematically as points or vectors. A system’s evolution traces a path through its state space.
Irreversibility: The inability of a process to return a system and its surroundings to their prior state without net change. Many macroscopic evolutions have a preferred direction despite often reversible microscopic laws.
Classical mechanics: The theory describing motion of macroscopic bodies using classical laws of motion. It predicts trajectories by evolving positions and momenta under forces.
Hamiltonian mechanics: A formulation of classical mechanics using generalized coordinates, momenta, and a Hamiltonian function. Hamilton’s equations specify continuous evolution through phase space.
Phase space: A space whose coordinates represent the positions and momenta of a classical system. Classical evolution is represented as a trajectory through phase space.