Title:
An Optimal transport point of view of Fluctuation theory.
Abstract:
The last decades the Fluctuation theory has been very successful
in describing the physic of processes out of equilibrium enjoying
a kind of structural stability also called “stochastic stability”.
While the physical concepts provide an accurate physical description
with universal relations ( Gallavotti-Cohen relation for example),
an unified formalism ( model-independent ) and a mathematical theory
is still missing. Meanwhile, the optimal transport theory’s school
has been developing a complete and rigorous theory of metric gradient
flow on probability spaces, which seems to be the natural framework
for the Fluctuation theory.
This talk will be an introduction to this optimal transport description
of the fluctuation theory for stochastic stable process, one of the
main argument being the correspondence between this framework and the
physical intuition.
We will present the main concepts and results as an introduction for
a work-group discussion on this topic.