Superstatistics
Encyclopedia
Superstatistics is a branch of statistical mechanics
or statistical physics
devoted to the study of non-linear and non-equilibrium
system
s. It is characterized by using the superposition
of multiple differing statistical model
s to achieve the desired non-linearity. In terms of ordinary statistical ideas, this is equivalent to compounding the distributions of random variables and it may be considered a simple case of a doubly stochastic model
.
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
or statistical physics
Statistical physics
Statistical physics is the branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic...
devoted to the study of non-linear and non-equilibrium
Stability theory
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions...
system
System
System is a set of interacting or interdependent components forming an integrated whole....
s. It is characterized by using the superposition
Superposition principle
In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually...
of multiple differing statistical model
Statistical model
A statistical model is a formalization of relationships between variables in the form of mathematical equations. A statistical model describes how one or more random variables are related to one or more random variables. The model is statistical as the variables are not deterministically but...
s to achieve the desired non-linearity. In terms of ordinary statistical ideas, this is equivalent to compounding the distributions of random variables and it may be considered a simple case of a doubly stochastic model
Doubly stochastic model
In statistics, a doubly stochastic model is a type of model that can arise in many contexts, but in particular in modelling time-series and stochastic processes....
.