Statistical fluctuations
Encyclopedia
Statistical fluctuations are fluctuations in quantities derived from many identical random processes. They are fundamental and unavoidable. It can be proved that the relative fluctuations reduce as the square root of the number of identical processes.
Statistical fluctuations are responsible for many results of statistical mechanics
and thermodynamics
, and phenomena such as shot noise in electronics.
of the number of processes.
many times and the number of heads and tails counted, the ratio of heads to tails will be very close to 1 (about as many heads as tails); but after only a few throws, outcomes with a significant excess of heads over tails or vice versa are common; if an experiment with a few throws is repeated over and over, the outcomes will fluctuate a lot.
An electric current
so small that not many electrons are involved flowing through a p-n junction
is susceptible to statistical fluctuations as the actual number of electrons per unit time (the current) will fluctuate; this produces detectable and unavoidable electrical noise known as shot noise
.
Statistical fluctuations are responsible for many results of statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
and thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
, and phenomena such as shot noise in electronics.
Description
When a number of random processes occur, it can be shown that the outcomes fluctuate (vary in time) and that the fluctuations are proportional to the square rootSquare root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
of the number of processes.
Examples
As an example that will be familiar to all, if a fair coin is tossedCoin flipping
Coin flipping or coin tossing or heads or tails is the practice of throwing a coin in the air to choose between two alternatives, sometimes to resolve a dispute between two parties...
many times and the number of heads and tails counted, the ratio of heads to tails will be very close to 1 (about as many heads as tails); but after only a few throws, outcomes with a significant excess of heads over tails or vice versa are common; if an experiment with a few throws is repeated over and over, the outcomes will fluctuate a lot.
An electric current
Electric current
Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...
so small that not many electrons are involved flowing through a p-n junction
P-n junction
A p–n junction is formed at the boundary between a P-type and N-type semiconductor created in a single crystal of semiconductor by doping, for example by ion implantation, diffusion of dopants, or by epitaxy .If two separate pieces of material were used, this would...
is susceptible to statistical fluctuations as the actual number of electrons per unit time (the current) will fluctuate; this produces detectable and unavoidable electrical noise known as shot noise
Shot noise
Shot noise is a type of electronic noise that may be dominant when the finite number of particles that carry energy is sufficiently small so that uncertainties due to the Poisson distribution, which describes the occurrence of independent random events, are of significance...
.
See also
- Thermal fluctuationsThermal fluctuationsIn statistical mechanics, thermal fluctuations are random deviations of a system from its equilibrium. All thermal fluctuations become larger and more frequent as the temperature increases, and likewise they disappear altogether as temperature approaches absolute zero.Thermal fluctuations are a...