Thermodynamic formalism for field-driven Lorentz gases

We analytically determine the dynamical properties of two-dimensional field-driven Lorentz gases within the thermodynamic formalism. For dilute gases subjected to an isokinetic thermostat, we calculate the topological pressure as a function of a temperaturelike parameter beta up to second order in the strength of the applied field. The Kolmogorov-Sinai entropy and the topological entropy can be extracted from a dynamical entropy defined as a Legendre transform of the topological pressure. Our calculations of the Kolmogorov-Sinai entropy exactly agree with previous calculations based on a Lorentz-Boltzmann equation approach. We give analytic results for the topological entropy and calculate the dimension spectrum from the dynamical entropy function.