Thermodynamic formalism for the Lorentz gas with open boundaries in $d$ dimensions

Details Thermodynamic formalism for the Lorentz gas with open boundaries in $d$ dimensions Thermodynamic formalism for the Lorentz gas with open boundaries in $d$ dimensions

2004-11-12

arxiv.org/abs/nlin/0411032v1

Phys. Rev. E 71, 036213 (2005)

Nonlinear Sciences

Chaotic Dynamics

7 pages, 5 figures

Scientific paper

10.1103/PhysRevE.71.036213

A Lorentz gas may be defined as a system of fixed dispersing scatterers, with a single light particle moving among these and making specular collisions on encounters with the scatterers. For a dilute Lorentz gas with open boundaries in $d$ dimensions we relate the thermodynamic formalism to a random flight problem. Using this representation we analytically calculate the central quantity within this formalism, the topological pressure, as a function of system size and a temperature-like parameter $\ba$. The topological pressure is given as the sum of the topological pressure for the closed system and a diffusion term with a $\ba$-dependent diffusion coefficient. From the topological pressure we obtain the Kolmogorov-Sinai entropy on the repeller, the topological entropy, and the partial information dimension.

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