Deterministic system

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

Physical laws that are described by differential equations 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.

The systems studied in chaos theory are deterministic. If the initial state were known exactly, then the future state of such a system could theoretically be predicted. However, in practice, knowledge about the future state is limited by the precision with which the initial state can be measured, and chaotic systems are characterized by a strong dependence on the initial conditions. This sensitivity to initial conditions can be measured with Lyapunov exponents.

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

A pseudorandom number generator is a deterministic algorithm, although its evolution is deliberately made hard to predict. A hardware random number generator, however, may be non-deterministic.

In economics, the Ramsey–Cass–Koopmans model is deterministic. The stochastic equivalent is known as Real Business Cycle theory.

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