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.

Examples

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.

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

A finite state machine may be either Deterministic finite automaton machine or non-deterministic.

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. Hardware Random Generators are cosidered non-deterministic because the infinitely small variations in intial conditions which are impossible to recreate and, therefore, reproduce a series of solutions. For example, think of a machine that can role dice by tossing them in the air and letting the role down an carpet covered inclined surface. The air temperature, humidity, slight variations in the movement of the machinery due to lubrication, non-uniformity of friction of the surface of the carpet, etc., will all have an impact on the outcome. However, the initial conditions of the system are finite and, therefore, if recreated, would result in the same output. Unfortunately, recreating these initial condition even once, let alone over a series of throws, is physically impossible.

See also

• Deterministic system (philosophy)
• Dynamical system
• Stochastic process