Volume 118, Number 2, April 2017
|Number of page(s)||7|
|Published online||20 June 2017|
Generalized fluctuation-dissipation theorem as a test of the Markovianity of a system
1 Department of Physics, Humboldt Universität zu Berlin - Newtonstr 15, 12489 Berlin, Germany
2 Raymond and Beverly Sackler School of Chemistry Tel Aviv University - Tel Aviv 6997801, Israel
3 Bernstein Center for Computational Neuroscience - Haus 2, Philippstr. 13, 10115 Berlin, Germany
Received: 23 March 2017
Accepted: 30 May 2017
We study how well a generalized fluctuation-dissipation theorem (GFDT) is suited to test whether a stochastic system is not Markovian. To this end, we simulate a stochastic non-equilibrium model of the mechanosensory hair bundle from the inner ear organ and analyze its spontaneous activity and response to external stimulation. We demonstrate that this two-dimensional Markovian system indeed obeys the GFDT, as long as i) the averaging ensemble is sufficiently large and ii) finite-size effects in estimating the conjugated variable and its susceptibility can be neglected. Furthermore, we test the GFDT also by looking only at a one-dimensional projection of the system, the experimentally accessible position variable. This reduced system is certainly non-Markovian and the GFDT is somewhat violated but not as drastically as for the equilibrium fluctuation-dissipation theorem. We explore suitable measures to quantify the violation of the theorem and demonstrate that for a set of limited experimental data it might be difficult to decide whether the system is Markovian or not.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 87.18.Tt – Noise in biological systems
© EPLA, 2017
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.