# Berlin 2018 – wissenschaftliches Programm

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# BP: Fachverband Biologische Physik

## BP 20: Statistical Physics of Biological Systems DY (joint session DY/BP)

### BP 20.13: Vortrag

### Mittwoch, 14. März 2018, 13:15–13:30, BH-N 333

**Estimation of the infinitesimal generator by square-root approximation** — •Luca Donati^{1}, Martin Heida^{2}, Bettina Keller^{1}, and Marcus Weber^{3} — ^{1}Freie Universität Berlin, Berlin, Germany — ^{2}WIAS, Berlin, Germany — ^{3}ZIB, Berlin, Germany

The dynamics of molecular systems can be represented by a continuous operator, called Propagator, that propagates probability densities with time. Associated to the Propagator, there exists another operator, called infinitesimal Generator, that defines the Fokker-Planck equation and provides information about the dynamics of the system in terms of transition rates between states. We have studied a method to obtain the discretized version of the Generator.

The method considers a Voronoi tasselleation of the conformational space and exploits the Gauss theorem to write the instantaneous rate between adjacent cells in terms of the Boltzmann weight of the intersecting surface. This quantity can be approximated by the geometric average of the Boltzmann weights of the cells.

We also show that there exists a direct correlation between the Generator and the potential energy function of the system. The method can be used to study the effect on dynamics of the system of small thermodynamic changes or perturbations of the potential energy function. We present results for 2d diffusion process and Alanine dipeptide.