On the relation between event-based and time-based current statistics

M. Esposito^1,2, K. Lindenberg² and I. M. Sokolov³

¹  Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles - Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium, EU
²  Department of Chemistry and Biochemistry and BioCircuits Institute, University of California, San Diego La Jolla, CA 92093-0340, USA
³  Institut für Physik, Humboldt-Universität zu Berlin - Newtonstrasse 15, D-12489 Berlin, Germany, EU

Received: 23 September 2009
Accepted: 11 December 2009

Abstract

Current statistics can be calculated in various ways. Event-based approaches use the statistics of the number of events occurring during a given time. Time-based approaches use the statistics of the time needed to reach a given number of events. By analyzing normal as well as anomalous statistics of nonequilibrium currents through a two level system in contact with two different reservoirs, we investigate the conditions under which these different statistics do or do not yield identical predictions. We rely on the continuous time random walk formulation introduced in our earlier work (Phys. Rev. E, 77 (2008) 051119).