Description: This article discusses the linear response of Hamiltonian chaotic systems as a function of the number of degrees of freedom. Abstract: Using numerical simulations we show that the response to weak perturbations of a variable of Hamiltonian chaotic systems depend on the number of degrees of freedom: When this is small (≈2) the response is not linear, in agreement with the well known objections to the Kubo linear response theory, while, for a larger number of degrees of freedom, the response becomes linear. This is due to the fact that increasing the number of degrees of freedom the shape of the distribution function, projected onto the subspace of the variable of interest, becomes fairly "regular."

Description: This article discusses chaos and thermal conductivity. Abstract: We argue that the condition of local thermal equilibrium realized several years ago by Rich and Visscher [Phys. Rev. B 11, 2164 (1975)] through a process of mathematical convergence can be obtained dynamically by adopting the prescription of a recent paper [M. Bianucci, R. Mannella, B.J. West, and P. Grigolini, Phys. Rev. E 51, 3002 (1995)]. This should contribute to shedding light on the still unsolved problem fo the microscopic derivation of the heat Fourier law.