Dr. U. Sharma (Freie Universität Berlin)
Wednesday, February 2, 2022 - 15:15
Online Event
Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar), --- ---
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Gradient flows is an important subclass of evolution equations, whose solution dissipates an energy 'as fast as possible'. This distinguishing feature endows these equations with a natural variational structure, which has received enormous attention over the last two decades. In recent years, it has become clear that if the gradient-flow equation originates from an underlying (reversible) stochastic particle system, then often the aforementioned variational structure is an exact decomposition of the large-deviation rate functional for the particle system. However, this decomposition and the corresponding gradient-flow structure breaks down if the underlying particles have additional non-dissipative effects (for instance in the case of non-reversible independent particles), even though the large-deviation rate functional is still available. Using the guiding example of independent non-reversible Markov jump particles, in this talk, I will discuss the various features of the rate functional and how it connects to relative entropy and Fisher information. Furthermore, I will show that if the underlying particle system is augmented with fluxes, then it is possible to derive gradient-flow-type structures in the non-reversible setting.
submitted by eismann (andrea.eismann@wias-berlin.de, 030 20372320)