Distributional Response to Biases in Deterministic Superdiffusion

TL;DR

This paper investigates how biases affect deterministic superdiffusion, revealing that the time-averaged velocity exhibits a distributional response characterized by the generalized arc-sine distribution, with ensemble averages remaining linear.

Contribution

It introduces the concept of distributional response to bias in deterministic superdiffusion and applies infinite ergodic theory to characterize the TAV distribution.

Findings

TAV is intrinsically random with a generalized arc-sine distribution.

Distributional limit theorem shows bias influences TAV distribution.

Ensemble-averaged TAV response remains linear.

Abstract

We report on a novel response to biases in deterministic superdiffusion. For its reduced map, we show using infinite ergodic theory that the time-averaged velocity (TAV) is intrinsically random and its distribution obeys the generalized arc-sine distribution. A distributional limit theorem indicates that the TAV response to a bias appears in the distribution, which is an example of what we term a distributional response induced by a bias. Although this response in single trajectories is intrinsically random, the ensemble-averaged TAV response is linear.