Predictability

Predictability

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Encyclopedia
Predictability is the degree to which a correct prediction
Prediction
A prediction or forecast is a statement about the way things will happen in the future, often but not always based on experience or knowledge...

 or forecast
Forecasting
Forecasting is the process of making statements about events whose actual outcomes have not yet been observed. A commonplace example might be estimation for some variable of interest at some specified future date. Prediction is a similar, but more general term...

 of a system
System
System is a set of interacting or interdependent components forming an integrated whole....

's state can be made either qualitatively or quantitatively.

Predictability and Causality


Causal determinism has a strong relationship with predictability. Perfect predictability implies strict determinism, but lack of predictability does not necessarily imply lack of determinism. Limitations on predictability could be caused by factors such as a lack of information or excessive complexity.

Laplace's Demon
Laplace's demon
In the history of science, Laplace's demon was the first published articulation of causal or scientific determinism by Pierre-Simon Laplace in 1814...

 is a supreme intelligence who could completely predict the one possible future given the Newtonian dynamical laws of classical physics and perfect knowledge of the positions and velocities of all the particles in the world.

In experimental physics, there are always observational errors determining variables such as positions and velocities. So perfect prediction is practically impossible. Moreover, in modern quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, Werner Heisenberg
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...

's indeterminacy principle puts limits on the accuracy with which such quantities can be known. So such perfect predictability is also theoretically impossible.

Predictability in Statistical Physics


Although the second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...

 can tell us about the equilibrium state that a system will evolve to, and steady state
Steady state
A system in a steady state has numerous properties that are unchanging in time. This implies that for any property p of the system, the partial derivative with respect to time is zero:...

s in dissipative system
Dissipative system
A dissipative system is a thermodynamically open system which is operating out of, and often far from, thermodynamic equilibrium in an environment with which it exchanges energy and matter....

s can sometimes be predicted, there exists no general rule to predict the time evolution
Time evolution
Time evolution is the change of state brought about by the passage of time, applicable to systems with internal state . 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...

 of systems far from equilibrium, e.g. chaotic systems, if they do not approach some kind of equilibrium. Their predictability usually deteriorates with time. To quantify predictability, the rate of divergence of system trajectories
Trajectory
A trajectory is the path that a moving object follows through space as a function of time. The object might be a projectile or a satellite, for example. It thus includes the meaning of orbit—the path of a planet, an asteroid or a comet as it travels around a central mass...

 in phase space
Phase space
In mathematics and physics, a phase space, introduced by Willard Gibbs in 1901, is a space in which all possible states of a system are represented, with each possible state of the system corresponding to one unique point in the phase space...

 can be measured (Kolmogorov-Sinai entropy, Lyapunov exponent
Lyapunov exponent
In mathematics the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories...

s).

Predictability in Mathematics


In stochastic analysis a random process
Stochastic process
In probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...

 is a predictable process
Predictable process
In stochastic analysis, a part of the mathematical theory of probability, a predictable process is a stochastic process which the value is knowable at a prior time...

if it is possible to know the "next" state at the present time.