Deterministic system

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In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system.^[1] A deterministic model will thus always produce the same output from a given starting condition or initial state.^[2]

In physics

Physical laws that are described by

represent deterministic systems, even though the state of the system at a given point in time may be difficult to describe explicitly.

In quantum mechanics, the Schrödinger equation, which describes the continuous time evolution of a system's wave function, is deterministic. However, the relationship between a system's wave function and the observable properties of the system appears to be non-deterministic.

In mathematics

The systems studied in

.

Markov chains and other random walks are not deterministic systems, because their development depends on random choices.

In computer science

A deterministic

, is a model of computation such that the successive states of the machine and the operations to be performed are completely determined by the preceding state.

A deterministic algorithm is an algorithm which, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states. There may be non-deterministic algorithms that run on a deterministic machine, for example, an algorithm that relies on random choices. Generally, for such random choices, one uses a pseudorandom number generator, but one may also use some external physical process, such as the last digits of the time given by the computer clock.

A pseudorandom number generator is a deterministic algorithm, that is designed to produce sequences of numbers that behave as random sequences. A hardware random number generator, however, may be non-deterministic.

Others

In economics, the Ramsey–Cass–Koopmans model is deterministic. The stochastic equivalent is known as real business-cycle theory.

See also

• Deterministic system (philosophy)
• Dynamical system
• Scientific modelling
• Statistical model
• Stochastic process

References