Relaxation, the Boltzmann-Jeans Conjecture and Chaos

Slow (logarithmic) relaxation from a highly excited state is studied in a Hamiltonian system with many degrees of freedom. The relaxation time is shown to increase as the exponential of the square root of the energy of excitation, in agreement with the Boltzmann-Jeans conjecture, while it is found to be inversely proportional to residual Kolmogorov-Sinai entropy, introduced in this Letter. The increase of the thermodynamic entropy through this relaxation process is found to be proportional to this quantity.