Thermodynamic formalism for field driven Lorentz gases

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.

9 pages, 5 figures

References in corpus (5)

• Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients
• Note on the Kaplan-Yorke dimension and linear transport coefficients
• Lyapunov Exponents from Kinetic Theory for a Dilute, Field-driven Lorentz Gas
• Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases I: Equilibrium Systems
• Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases II: Open Systems

Cited by in corpus (5)

• Spacetime structures of continuous time quantum walks
• Slow transport by continuous time quantum walks
• Large deviations of Lyapunov exponents
• Investigation of continuous-time quantum walk by using Krylov subspace-Lanczos algorithm
• Thermodynamic formalism for the Lorentz gas with open boundaries in $d$ dimensions