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Volume 5, Issue 5
Brownian Motion and Entropy Growth on Irregular Surfaces

C. Chevalier & F. Debbasch

Int. J. Numer. Anal. Mod., 5 (2008), pp. 36-46.

Published online: 2018-11

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  • Abstract

Many situations of physical and biological interest involve diffusions on manifolds. It is usually assumed that irregularities in the geometry of these manifolds do not influence diffusions. The validity of this assumption is put to the test by studying Brownian motions on nearly flat 2D surfaces. It is found by perturbative calculations that irregularities in the geometry have a cumulative and drastic influence on diffusions, and that this influence typically grows exponentially with time. The corresponding characteristic times are computed and discussed. Conditional entropies and their growth rates are considered too.

  • Keywords

Brownian motion, stochastic processes on manifolds, lateral diffusions.

  • AMS Subject Headings

60J65, 8J65, 60-xx: 60Gxx, 82Cxx: 82C70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-5-36, author = {C. Chevalier and F. Debbasch}, title = {Brownian Motion and Entropy Growth on Irregular Surfaces}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2018}, volume = {5}, number = {5}, pages = {36--46}, abstract = {

Many situations of physical and biological interest involve diffusions on manifolds. It is usually assumed that irregularities in the geometry of these manifolds do not influence diffusions. The validity of this assumption is put to the test by studying Brownian motions on nearly flat 2D surfaces. It is found by perturbative calculations that irregularities in the geometry have a cumulative and drastic influence on diffusions, and that this influence typically grows exponentially with time. The corresponding characteristic times are computed and discussed. Conditional entropies and their growth rates are considered too.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/838.html} }
TY - JOUR T1 - Brownian Motion and Entropy Growth on Irregular Surfaces AU - C. Chevalier & F. Debbasch JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 36 EP - 46 PY - 2018 DA - 2018/11 SN - 5 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/838.html KW - Brownian motion, stochastic processes on manifolds, lateral diffusions. AB -

Many situations of physical and biological interest involve diffusions on manifolds. It is usually assumed that irregularities in the geometry of these manifolds do not influence diffusions. The validity of this assumption is put to the test by studying Brownian motions on nearly flat 2D surfaces. It is found by perturbative calculations that irregularities in the geometry have a cumulative and drastic influence on diffusions, and that this influence typically grows exponentially with time. The corresponding characteristic times are computed and discussed. Conditional entropies and their growth rates are considered too.

C. Chevalier and F. Debbasch. (2018). Brownian Motion and Entropy Growth on Irregular Surfaces. International Journal of Numerical Analysis and Modeling. 5 (5). 36-46. doi:
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