Laboratoire Matière et Systèmes complexes

UMR 7057 Université Paris Diderot-CNRS

Bâtiment Condorcet

10 rue Alice Domont et Léonie Duquet

75205 Paris cedex 13

France

Phone: +33 (0)1 57 27 70 64

Fax : +33 (0)1 57 27 62 11

e-mail : Julien.Tailleur (AT) univ-paris-diderot.fr

UMR 7057 Université Paris Diderot-CNRS

Bâtiment Condorcet

10 rue Alice Domont et Léonie Duquet

75205 Paris cedex 13

France

Phone: +33 (0)1 57 27 70 64

Fax : +33 (0)1 57 27 62 11

e-mail : Julien.Tailleur (AT) univ-paris-diderot.fr

Defended on the 8th of October 2007 (pdf, slides)

My thesis was dedicated to the study of some applications of large deviation theory lying at the frontier between dynamical systems and out of equilibrium statistical mechanics. As a systematic tool to quantify the probability of rare events, large deviation functions indeed find many uses, either to reveal rare interesting structures or to extend the notion of thermodynamic potentials to non-equilibrium situations. As I was required by the administration to summarize my works in 1,000 letters, I reproduce below the "result" of this exercise. However, if you really want to know what I did during the three last years and can read french, I strongly advise you to read the three pages of introduction (that you can find here) at the begining of the manuscript :-)

My thesis was dedicated to the study of some applications of large deviation theory lying at the frontier between dynamical systems and out of equilibrium statistical mechanics. As a systematic tool to quantify the probability of rare events, large deviation functions indeed find many uses, either to reveal rare interesting structures or to extend the notion of thermodynamic potentials to non-equilibrium situations. As I was required by the administration to summarize my works in 1,000 letters, I reproduce below the "result" of this exercise. However, if you really want to know what I did during the three last years and can read french, I strongly advise you to read the three pages of introduction (that you can find here) at the begining of the manuscript :-)

__________________ /| /| | | ||__|| | Summary | / O O\__ of | / \ my | / \ \ Thesis | / _ \ \ ______________| / |\____\ \ || / | | | |\____/ || / \|_|_|/ | __|| / / \ |____| || / | | /| | --| | | |// |____ --| * _ | |_|_|_| | \-/ *-- _--\ _ \ // | / _ \\ _ // | / * / \_ /- | - | | * ___ c_c_c_C/ \C_c_c_c

The theory of large deviations deals with the asymptotic scaling of
rare events. It is the modern framework of equilibrium statistical
physics and seems to offer a natural extension to out-of-equilibrium
situations. We present in this thesis some applications of this theory
in different contexts. First, we show how to detect numerically
trajectories of atypical chaoticity in large dimensional dynamical
systems. We then extend the algorithm to a larger class of
systems/observables. In the second part, we show how the computation
of large deviation functions for an out-of-equilirbrium system can
sometimes be reduced to an equilibrium computation. The last part
deals with the numerical determination of reaction paths in chemistry.
A supersymmetric approach of the Fokker-Planck equation naturally
leads to a numerical implementation of this project, it also provides
a simple way to rederive Morse theory, a main tool in algebraic
topology.

Last modified: Fri Feb 29 18:16:10 CET 2008