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A Concise Introduction to the Statistical Physics of Complex Systems pp 33–57Cite as

Non-stationary Dynamics and Stochastic Formalism

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Part of the book series: SpringerBriefs in Complexity ((BRIEFSCOMPLEXITY))

Abstract

In the first part of this book, we have considered the stationary properties of physical systems composed of a large number of particles, using as fundamental statistical object the joint distribution of all the degrees of freedom of the system (for instance positions and velocities, or spin variables). This steady state is expected to be reached after a transient regime, during which the macroscopic properties of the system evolve with time. Describing the statistical state of the system during this transient regime is also certainly of interest.

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Notes

  1. 1.

    Note that from this definition, \(\Upgamma\) is of the order of \(C(0)\tau_{{\rm col}}.\) For \(\Upgamma\) to be finite in the limit of a small \(\tau_{{\rm col}},\) one also needs to assume that \(C(0) \propto 1/\tau_{{\rm col}}.\)

References

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  3. V.V. Petrov, Sums of Independent Random Variables (Springer, Berlin, 1975)

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  4. W. Feller, An Introduction to Probability Theory and its Applications. vol. I, (Wiley, New York, 1966)

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  5. E. Bertin, F. Bardou, Am. J. Phys. 76, 630 (2008)

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Authors and Affiliations

  1. Laboratoire de Physique, Ecole Normale Supérieure de Lyon, 46 allée d’Italie, 69364, Lyon, France

    Eric Bertin

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  1. Eric Bertin
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Bertin, E. (2012). Non-stationary Dynamics and Stochastic Formalism. In: A Concise Introduction to the Statistical Physics of Complex Systems. SpringerBriefs in Complexity. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23923-6_2

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  • DOI: https://doi.org/10.1007/978-3-642-23923-6_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23922-9

  • Online ISBN: 978-3-642-23923-6

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

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