Regensburg 2022 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 44: Poster Session: Statistical Physics and Critical Phenomena

DY 44.10: Poster

Thursday, September 8, 2022, 15:00–18:00, P2

Coarse-graining of systems with discrete Markovian dynamics — Stefan Klumpp and •Miguel Rodríguez Martín — Institute for the Dynamics of Complex Systems, University of Göttingen, Göttingen.

There exists a wide range of physical systems that can be described by discrete Markovian dynamics. In many cases it is desirable to reduce the number of states in order to lower the computational cost or obtain an effective description that captures the most relevant effects at a given scale. A steady state-conserving method of coarse graining based on merging adjacent states and obtaining new transition rates from the optimization of the Kullback-Leibler divergence is generalized by minimizing the Rényi divergence instead. The resulting transition rates depend on the quotients between the steady state probabilities of the merged states in the original system, so a method is developed to compute these transition rates without the need of finding the steady state probabilities. Making use of the similarities between the master equation and Schrödinger's equation, a formulation for classical discrete Markov processes analogous to quantum mechanics is developed, both in the frame of Schrödinger's formulation and second quantization. These are used to study coarse graining under the constraint that the steady state must be conserved.