Time-Scales for the Approach to Thermal Equilibrium
The approach to equilibrium of an isolated system constitutes the basic principle of thermodynamics. Fermi, Pasta and Ulam (FPU) studied numerically this process for a chain of coupled oscillators. The FPU “experiment” has been an amazingly rich source of problems in modern dynamical system theory and has played in this context a role analogue to the Ising model for statistical mechanics. Recent results have shown the presence of increasingly long time-scales of the relaxation process as the energy is lowered. States which were previously classified as “frozen” have been instead discovered to “diffuse” very slowly to the equipartition state. The dependence of the diffusive time-scale TD on energy E and number of degrees of freedom N has been found both analytically and numerically for some classes of initial conditions. For “thermodynamical” initial states TD is found to scale at small E with an inverse power-law of E = E/N.
KeywordsLyapunov Exponent Thermodynamic Limit Primary Resonance Critical Energy Density Energy Equipartition
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