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Thermodynamic formalism for field driven Lorentz gases

Oliver Muelken·Henk van Beijeren
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Abstract

We analytically determine the dynamical properties of two dimensional field driven Lorentz gases within the thermodynamic formalism. For dilute gases subjected to an iso-kinetic thermostat, we calculate the topological pressure as a function of a temperature-like parameter $\ba$ 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.

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Oliver Muelken, Henk van Beijeren. 2003-12-22. Thermodynamic formalism for field driven Lorentz gases. https://doi.org/10.1103/physreve.69.046203

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