Geometry of Optimal Mass Transport, where Probability, Control, and Physics Meet

Optimal Mass Transport (OMT) was conceived more than two centuries ago by Gaspar Monge (1781) as the mathematical problem to transfer mass between source and target distributions, while incurring minimal transportation cost. It naturally evolved into a topic in economics where transference of resources between producers and consumers is of great practical significance; in this, it provided the context for the development of duality theory and linear programming (Leonid Kantorovich 1940). In the past thirty years, OMT has opened up important new chapters in Probability Theory and the Physical Sciences. In this talk, after a sketchy overview of OMT, we will explain its relevance in quantifying energy dissipation in thermodynamic transitions. Specifically, we will focus on bounding the power that can be drawn from stochastic models of thermodynamic engines that operate between heat baths of unequal or possibly varying temperature, and derive physically meaningful expressions for the dissipation cost of cycling over a finite time window.

The talk is based on joint works with Rui Fu (UCI), Amir Taghvaei (UCI) and Yongxin Chen (GaTech).
Research funding by NSF and AFOSR is gratefully acknowledged.

Please join the event.

About Tryphon Georgiou

Tryphon T. Georgiou was educated at the National Technical University of Athens, Greece, and the University of Florida, Gainesville (PhD 1983). He is currently a Distinguished Professor of Mechanical and Aerospace Engineering at the University of California, Irvine. He is also Professor Emeritus at the University of Minnesota, where he held the Hermes-Luh Chair (2002-2016) and served as co-director of the Control Science and Dynamical Systems Center (1990-2016). Dr. Georgiou is a Fellow of the IEEE, IFAC, and a Foreign Member of the Royal Swedish Academy of Engineering Sciences (IVA).