Science, Engineering and Food Science
Prof. Alexander Mielke (WIAS & HU Berlin) will give a lecture on entropy-induced geometry for classical and quantum Markov semigroups.
Speaker: Prof. Alexander Mielke (Weierstrass Institute for Applied Analysis and Stochastics (WIAS) and Humboldt University of Berlin) Title: Entropy-induced geometry for classical and quantum Markov semigroups Abstract: About two decades ago Felix Otto introduced his program to interpret diffusion equations as gradient flows with respect to the Wasserstein metric, which culminated in the fundamental paper "The geometry of dissipative evolution equations: the porous medium equation" (2001). This generated a wide variety of new tools for large classes of dissipative processes. In particular, surprising nonlinear tools for the study of linear semigroups developed. In this talk we will show how that the Kolmogorov forward equations for reversible Markov processes can be understood as a gradient flow with the Boltzmann entropy as a driving functional. For quantum mechanical applications we consider Lindblad equation satisfying a detailed balance condition and construct a dissipation metric of Kubo-Mori type such that the dissipative part of the Lindbladian has again a gradient structure.
Throughout, we will hint at our main motivation that has its basis in deriving of thermodynamically consistent models coupling different dissipative mechanisms such as heat transfer, reaction, diffusion, or quantum scattering. About the Speaker: Alexander Mielke is a Full Professor of Mathematics at the Humboldt University of Berlin and Head of the Research Group “Partial Differential Equations” at the Weierstrass Institute for Applied Mathematics and Stochastics. He is author/editor of 8 books and has published more than 140 articles in peer-reviewed journals. Moreover he has (co-)organized more than 50 workshops & conferences and is involved in many funded research projects, in particular as Project Head of the European Research Council Advanced Grant Analysis of Multiscale Systems Driven by Functionals. Further details on the speaker are available at https://www.wias-berlin.de/people/mielke/
|Category:||Public Lectures and Seminars: Science Engineering and Food Science|
|Time:||3pm - 4pm|
|Location:||Western Gateway Building Room 226|
|Target Audience:||General mathematical audience|
|Admission Price: €||Free|
021 420 5856