Department of Mathematical Sciences, Ritsumeikan University Web Page

Geometry Seminar

Title :
Thermodynamics and information geometry via contact geometry

Speaker :
Shin-itiro Goto (Kyoto University)

14:00-15:30, August 23, 2016
Room: Biwako-Kusatsu Campus (BKC), West Wing, 7th floor, 1st Laboratory of Mathematics

Abstract :
In this talk we discuss firstly
a geometric description of nonequilibrium thermodynamics,  
and discuss secondly how to relate information geometry to contact geometry.
For the first one, attention is drawn to formulating a class of
relaxation processes as that of dynamical systems on a contact manifold.
In addition it is shown that such dynamical systems include an existing
dynamical system derived in physics. Then, an explicit form of an
invariant measure for these dynamical systems on the contact manifold is shown.
For the second one, it is shown how a contact manifold and a
strictly convex function on the manifold induce a dually flat space
developed in information geometry.