Editing Time evolution (section)

{{Short description|Change of state over time, especially in physics}}

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'''Time evolution''' is the change of state brought about by the passage of [[time]], applicable to systems with internal state (also called ''stateful systems''). In this formulation, ''time'' is not required to be a continuous parameter, but may be [[discrete time|discrete]] or even [[wiktionary:finite|finite]]. In [[classical physics]], time evolution of a collection of [[rigid body|rigid bodies]] is governed by the principles of [[classical mechanics]]. In their most rudimentary form, these principles express the relationship between forces acting on the bodies and their acceleration given by [[Newton's laws of motion]]. These principles can be equivalently expressed more abstractly by [[Hamiltonian mechanics]] or [[Lagrangian mechanics]].

The concept of time evolution may be applicable to other stateful systems as well. For instance, the operation of a [[Turing machine]] can be regarded as the time evolution of the machine's control state together with the state of the tape (or possibly multiple tapes) including the position of the machine's read-write head (or heads). In this case, time is considered to be discrete steps.

Stateful systems often have dual descriptions in terms of states or in terms of [[observable]] values. In such systems, time evolution can also refer to the change in observable values. This is particularly relevant in [[quantum mechanics]] where the [[Schrödinger picture]] and [[Heisenberg picture]] are (mostly){{Clarification needed|date=December 2023}} equivalent descriptions of time evolution.