Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 66: Poster: Stat. Phys. (Gen., Critical Phen., Biol.)

DY 66.9: Poster

Thursday, March 15, 2018, 15:30–18:00, Poster A

Occupation time statistics for single molecule dynamics — •Alessio Lapolla and Aljaz Godec — Mathematical Biophysics Group, Max-Planck-Institute for Biophysical Chemistry (Göttingen)

State-of-the art experimental methods nowadays routinely probe dynamical properties of individual molecules, and thereby provide unprecedented insight into biophysical phenomena at low-copy numbers. Yet, despite the consensus about its relevance, a general theory of single molecule dynamics remains elusive.

Namely, most available experimental techniques are limited by short, typically subergodic observation times. As a result, their interpretation cannot rely neither on ensemble statistical mechanics nor ergodic theory. This poses the need for a statistical mechanics of time-averaged observables, explicitly taking into account the fluctuations between different realizations.

In our work we focused on the statistics of occupation time: the fraction of time a random process spends in any given region of configuration space. We obtained rigorous general results for the lower order moments of the occupation time in Markovian dynamics, which go beyond large-deviation theory. To illustrate the predictive power of the theory we provide exact results for a selection of simple diffusive models of single-molecule dynamics.