Heat conductivity and dynamical instability

We present a series of numerical and analytical computations on heat conduc tion for a strongly chaotic system-the Lorentz gas. Heat conduction is char acterized by nontrivial features: While the heat conductivity is well defin ed in the thermodynamic limit, a linear gradient appears only for quite sma ll temperature differences. The key dynamical feature inducing such a behav ior is recognized as deterministic diffusion (along transport direction) wh ich is usually associated to full hyperbolicity. [S0031-9007(99)08614-7].