Entropy production for open dynamical systems

The concept of the conditional probability density is used to define a specific entropy for open dynamical systems exhibiting transient chaos. The production of entropy turns out to be proportional to the difference of the escape rate and the sum of all averaged Lyapunov exponents on the saddle governing the dynamics. The single-particle transport proper-ties do not depend on the microscopic details provided the dynamical systems produce the same entropy. The dimension of the unstable foliation of the saddle is shown to be identical in all microscopic single-particle models of the same transport process.