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 - <p style="text-align: justify;">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.</p>