Relaxation, the Boltzmann-Jeans conjecture, and chaos - art. no. 055205

Slow (logarithmic) relaxation from a highly excited state is studied in a H amiltonian system with many degrees of freedom. The relaxation time is show n to increase as the exponential of the square root of the energy of excita tion, in agreement with the Boltzmann-Jeans conjecture. while it is found t o be inversely proportional to residual Kolmogorov-Sinai entropy, introduce d in this Rapid Communication. The increase of the thermodynamic entropy th rough this relaxation process is found to be proportional to this quantity.