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 In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic be ...

and thermodynamics, including phenomena such as

shot noise Shot noise or Poisson noise is a type of noise which can be modeled by a Poisson process. In electronics shot noise originates from the discrete nature of electric charge. Shot noise also occurs in photon counting in optical devices, where sho ...

in electronics.

Description

When a number of

random 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 ...

processes occur, it can be shown that the outcomes fluctuate (vary in time) and that the fluctuations are inversely proportional to the square root of the number of processes.

Examples

As an example that will be familiar to all, if a fair coin is tossed 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

Description

Examples

See also