Zeitschrift für Physik B Condensed Matter

, Volume 29, Issue 3, pp 265–272 | Cite as

Structural modeling of diffusion processes

  • A. Bach
  • D. Dürr
Article
Received:

Abstract

We try to give a stochastic description for a system which is in contact with a reservoir if the deterministic phenomenological description is given. We compare the phenomenological method, i.e. the enlargement of the phenomenological equation by stochastic parts leading to a stochastic differential equation and the reduction of the microscopic description in the scope of classical physics. The projector method gives a description of the system by a Fokker-Planck equation. The essential facts characterizing a diffusion process are extracted from the structure of these equations. If the systematic part of the phenomenological equation can be derived from generalized Poisson brackets it is possible to give criteria for an ansatz of a stochastic description which is self consistent and in accordance with the results of information theory.

Keywords

Differential Equation Neural Network Complex System Information Theory Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • A. Bach
    • 1
  • D. Dürr
    • 1
  1. 1.Institut für theoretische Physik IUniversität MünsterMünster/WestfalenGermany

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