Current-activity versus local-current fluctuations in driven flow with exclusion

TL;DR

This paper investigates fluctuations in the steady-state current activity and local current in a one-dimensional exclusion process, revealing how sampling methods influence observed scaling behaviors and distribution asymmetries.

Contribution

It demonstrates that instantaneous activity sampling masks anomalous scaling effects and reconciles conflicting results on distribution skewness in different phases.

Findings

Cumulants of activity and local current behave similarly except in maximal-current phase.

Instantaneous activity sampling overshadows non-equal time correlation effects.

Distribution skewness varies with phase, being positive in low-current and negative elsewhere.

Abstract

We consider fluctuations of steady-state current activity, and of its dynamic counterpart, the local current, for the one-dimensional totally asymmetric simple exclusion process. The cumulants of the integrated activity behave similarly to those of the local current, except that they do not capture the anomalous scaling behavior in the maximal-current phase and at its boundaries. This indicates that the systemwide sampling at equal times, characteristic of the instantaneous activity, overshadows the subtler effects which come about from non-equal time correlations, and are responsible for anomalous scaling. We show that apparently conflicting results concerning asymmetry (skewness) of the corresponding distributions can in fact be reconciled, and that (apart from a few well-understood exceptional cases) for both activity and local current one has positive skew deep within the low-current phase, and negative skew everywhere else.