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Universität Augsburg
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Universität Augsburg
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Dr. Michiel Renger
(TUM)
spricht am
Donnerstag, 24. November 2022
um
17:15 Uhr
im
TUM, Boltzmann-3, Garching, Raum 03.08.011, Etage 3
über das Thema:
| Abstract: |
| Often thermodynamical phenomena are described microscopically by a randomly evolving particle system, or macroscopically by an evolution equation, and the two levels of description are connected by sending the number of particles to infinity. Onsager and Machlup postulated that microscopic systems in detailed balance (reversible Markov process) behave as a gradient flow on the macroscopic level. This principle is now well-understood and can be made precise via the theory of large deviations. In order to understand the behaviour of non-equilibrium systems (not in detailed balance/nonreversible), one commonly studies particle densities as well as particle fluxes; this is the topic of Macroscopic Fluctuation Theory. Classically the large deviations yield a natural Hilbert structure that allows to decompose the dynamics into a gradient flow component (dissipating free energy) and a Hamiltonian component (conserving energy). For systems where the particles hop between discrete sites, and the macroscopic equation is a system of ODEs, such natural Hilbert space is not available. We present a generalised Macroscopic Fluctuation Theory, sufficiently general to apply to, for example zero-range processes and chemical reactions. This work lies on the boundary between probability, analysis and physics, but I will mostly focus on the analysis and physics part. |
| Hierzu ergeht herzliche Einladung. |