Definitions for superstatistics
su·per·statis·tics

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1. superstatisticsnoun

   A branch of statistical mechanics that studies certain nonlinear systems

WikipediaRate this definition:0.0 / 0 votes

1. Superstatistics

   Superstatistics is a branch of statistical mechanics or statistical physics devoted to the study of non-linear and non-equilibrium systems. It is characterized by using the superposition of multiple differing statistical models 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. Consider an extended thermodynamical system which is locally in equilibrium and has a Boltzmann distribution, that is the probability of finding the system in a state with energy E {\displaystyle E} is proportional to exp ⁡ ( − β E ) {\displaystyle \exp(-\beta E)} . Here β {\displaystyle \beta } is the local inverse temperature. A non-equilibrium thermodynamical system is modeled by considering macroscopic fluctuations of the local inverse temperature. These fluctuations happen on time scales which are much larger than the microscopic relaxation times to the Boltzmann distribution. If the fluctuations of β {\displaystyle \beta } are characterized by a distribution f ( β ) {\displaystyle f(\beta )} , the superstatistical Boltzmann factor of the system is given by B ( E ) = ∫ 0 ∞ d β f ( β ) exp ⁡ ( − β E ) . {\displaystyle B(E)=\int _{0}^{\infty }d\beta f(\beta )\exp(-\beta E).} This defines the superstatistical partition function Z = ∑ i = 1 W B ( E i ) {\displaystyle Z=\sum _{i=1}^{W}B(E_{i})} for system that can assume discrete energy states { E i } i = 1 W {\displaystyle \{E_{i}\}_{i=1}^{W}} . The probability of finding the system in state E i {\displaystyle E_{i}} is then given by p i = 1 Z B ( E i ) . {\displaystyle p_{i}={\frac {1}{Z}}B(E_{i}).} Modeling the fluctuations of β {\displaystyle \beta } leads to a description in terms of statistics of Boltzmann statistics, or "superstatistics". For example, if β {\displaystyle \beta } follows a Gamma distribution, the resulting superstatistics corresponds to Tsallis statistics. Superstatistics can also lead to other statistics such as power-law distributions or stretched exponentials. One needs to note here that the word super here is short for superposition of the statistics. This branch is highly related to the exponential family and Mixing. These concepts are used in many approximation approaches, like particle filtering (where the distribution is approximated by delta functions) for example.

WikidataRate this definition:0.0 / 0 votes

1. Superstatistics

   Superstatistics is a branch of statistical mechanics or statistical physics devoted to the study of non-linear and non-equilibrium systems. It is characterized by using the superposition of multiple differing statistical models 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. Consider an extended thermodynamical system which is locally in equilibrium and has a Boltzmann distribution, that is the probability of finding the system in a state with energy is proportional to . Here is the local inverse temperature. A non-equilibrium thermodynamical system is modeled by considering macroscopic fluctuations of the local inverse temperature. These fluctuations happen on time scales which are much larger than the microscopic relaxation times to the Boltzmann distribution. If the fluctuations of are characterized by a distribution, the superstatistical Boltzmann factor of the system is given by This defines the superstatistical partition function where the system can assume discrete energy states . The probability of finding the system in state is then given by

How to pronounce superstatistics?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say superstatistics in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of superstatistics in Chaldean Numerology is: 6

2. Pythagorean Numerology

   The numerical value of superstatistics in Pythagorean Numerology is: 2

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Superstatistics
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Superstatistics
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=superstatistics