In
mathematics,
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...
and
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, a deterministic system is a system in which no
randomness
In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual rand ...
is involved in the development of future states of the system. A deterministic
model
A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure.
Models c ...
will thus always produce the same output from a given starting condition or initial state.
Dynamical systems
at Scholarpedia
''Scholarpedia'' is an English-language wiki-based online encyclopedia with features commonly associated with open-access online academic journals, which aims to have quality content in science and medicine.
''Scholarpedia'' articles are written ...
In physics
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
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistr ...
, the Schrödinger equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...
, which describes the continuous time evolution of a system's wave function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...
, is deterministic. However, the relationship between a system's wave function and the observable
In physics, an observable is a physical quantity that can be measured. Examples include position and momentum. In systems governed by classical mechanics, it is a real-valued "function" on the set of all possible system states. In quantum phy ...
properties of the system appears to be non-deterministic.
In mathematics
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 walk
In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space.
An elementary example of a random walk is the random walk on the integer number line \mathbb Z ...
s are not deterministic systems, because their development depends on random choices.
In computer science
A deterministic model of computation
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes how ...
, for example a deterministic Turing machine, 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
In computer science, a deterministic algorithm is an algorithm that, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states. Deterministic algorithms are by far ...
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
A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generate ...
, 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
In computing, a hardware random number generator (HRNG) or true random number generator (TRNG) is a device that generates random numbers from a physical process, rather than by means of an algorithm. Such devices are often based on microscopic ...
, however, may be non-deterministic.
Others
In economics, the Ramsey–Cass–Koopmans model
The Ramsey–Cass–Koopmans model, or Ramsey growth model, is a neoclassical model of economic growth based primarily on the work of Frank P. Ramsey, with significant extensions by David Cass and Tjalling Koopmans. The Ramsey–Cass–Koopmans ...
is deterministic. The stochastic equivalent is known as real business-cycle theory
Real business-cycle theory (RBC theory) is a class of new classical macroeconomics models in which business-cycle fluctuations are accounted for by real (in contrast to nominal) shocks. Unlike other leading theories of the business cycle, RBC th ...
.
See also
* Deterministic system (philosophy)
A deterministic system is a conceptual model of the philosophical doctrine of determinism applied to a system for understanding everything that has and will occur in the system, based on the physical outcomes of causality. In a deterministic syste ...
* Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in ...
* Scientific modelling
Scientific modelling is a scientific activity, the aim of which is to make a particular part or feature of the world easier to understand, define, quantify, visualize, or simulate by referencing it to existing and usually commonly accepted ...
* Statistical model
* Stochastic process
References
{{Reflist
System
Dynamical systems