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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 or even finite. In classical physics, time evolution of a collection of 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] equivalent descriptions of time evolution.
Timeevolution is the change of state brought about by the passage of time, applicable to systems with internal state (also called stateful systems). In...
U(t)=e^{-iHt/\hbar }} is known as the time-evolution operator, and has the crucial property that it is unitary. This timeevolution is deterministic in the sense...
Evolution is the change in the heritable characteristics of biological populations over successive generations. It occurs when evolutionary processes...
{e} ^{\pm \mathrm {i} H_{0,{\text{S}}}t/\hbar }} by the corresponding time-evolution operator in the definitions below. Let | ψ S ( t ) ⟩ = e − i H S t /...
=H(t)|\psi (t)\rangle } Equivalently, the timeevolution postulate can be stated as: Postulate III The timeevolution of a closed system is described by a...
used to describe the timeevolution of a system that can be modeled as being in a probabilistic combination of states at any given time, and the switching...
Koopman and John von Neumann: the timeevolution of the Wigner function approaches, in the limit ħ → 0, the timeevolution of the Koopman–von Neumann wavefunction...
}^{\alpha }} can be appropriately called the shape gradient of area. An evolution governed by C ≡ B α α {\displaystyle C\equiv B_{\alpha }^{\alpha }} is...
Evolutionism is a term used (usually derogatorily) to denote the theory of evolution. Its exact meaning has changed over time as the study of evolution...
the evolution of the state variables. In physics, a dynamical system is described as a "particle or ensemble of particles whose state varies over time and...
Human evolution is the evolutionary process within the history of primates that led to the emergence of Homo sapiens as a distinct species of the hominid...
paradox) is a feature of quantum-mechanical systems allowing a particle's timeevolution to be slowed down by measuring it frequently enough with respect to...
solution to the problem of time. It is a bit more subtle than this. Although without constraints and having "general evolution", the latter is only in terms...
is to consider the time-evolution of the expected position and expected momentum, which can then be compared to the time-evolution of the ordinary position...
series, formulated by Freeman Dyson, is a perturbative expansion of the timeevolution operator in the interaction picture. Each term can be represented by...
evolves in time (see also the Belavkin equation for the evolution under continuous measurement). This uses the Schrödinger picture, where evolution of the...
"world tube" (the timeevolution of a closed surface) that cannot be continuously deformed (shrunk) to a world line (the timeevolution of a point or observer)...
travel based upon quantum mechanics requires physicists to solve the timeevolution equations for density states in the presence of closed timelike curves...
outline is provided as an overview of and topical guide to evolution: In biology, evolution is change in the heritable characteristics of biological organisms...
realistic situation. The diffusion equation yields an approximation of the timeevolution of the probability density function associated with the position of...
1951 book Time's Arrow and Evolution discusses "the relationship between time's arrow (the second law of thermodynamics) and organic evolution." This influential...
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