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How do stochastic processes enter into physics?

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Stochastic Processes — Mathematics and Physics II

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1250))

Abstract

Fluctuations in non-equilibrium systems do not arise from a probability distribution of the initial state, but are continually generated by the equations of motion. In order to derive them from statistical mechanics a drastic repeated randomness assumption is indispensable. One is then led to a master equation, from which both the deterministic macroscopic equation and the fluctuations are obtained by a limiting process. The approximate nature of the whole procedure makes the use of strictly mathematical delta-correlations and Itô calculus illusory.

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Authors and Affiliations

  1. Institut für Theoretische Physik, R.W.T.H. Aachen, Templergraben 55, 5100, Aachen, Germany

    N. G. van Kampen

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  1. N. G. van Kampen
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Sergio Albeverio Philippe Blanchard Ludwig Streit

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© 1987 Springer-Verlag

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van Kampen, N.G. (1987). How do stochastic processes enter into physics?. In: Albeverio, S., Blanchard, P., Streit, L. (eds) Stochastic Processes — Mathematics and Physics II. Lecture Notes in Mathematics, vol 1250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077353

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  • DOI: https://doi.org/10.1007/BFb0077353

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17797-5

  • Online ISBN: 978-3-540-47835-5

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