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We report on a novel response to biases in deterministic superdiffusion. Forits reduced map, we show using infinite ergodic theory that the time-averagedvelocity (TAV) is intrinsically random and its distribution obeys thegeneralized arc-sine distribution. A distributional limit theorem indicatesthat the TAV response to a bias appears in the distribution, which is anexample of what we term a distributional response induced by a bias. Althoughthis response in single trajectories is intrinsically random, theensemble-averaged TAV response is linear.

Distributional Response to Biases in Deterministic Superdiffusion