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

TL;DR

This paper explores the relationship between event-based and time-based current statistics in nonequilibrium systems, analyzing conditions under which they produce identical or different predictions using a continuous time random walk framework.

Contribution

It provides a detailed analysis of when event-based and time-based current statistics align or differ in nonequilibrium two-level systems.

Findings

Event-based and time-based statistics can yield different results under certain conditions.

Analysis of normal and anomalous current statistics reveals specific scenarios of equivalence.

Utilizes a continuous time random walk model to compare statistical approaches.

Abstract

Current statistics can be calculated in various ways. Event-based approaches use the statistics of the number of events occuring 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, 051119 (2008)].