Transient chaos: The origin of transport in driven systems

In open Hamiltonian systems transport is governed by chaotic saddles which are low-dimensional if a single-particle description can be used. We show that in systems where the motion of the particle is biased towards one direction, the chaotic set is never space filling. Its escape rate splits into two parts: a) a term proportional to the square of the bias; b) a term also present in the non-driven case which vanishes in the large system limit. These general results are equivalent to previous ones on thermostatted systems if the systems have identical entropy production.