Irreversible energy transfer and distribution in complex systems

Abstract

This presentation examines the conditions under which irreversible energy transfer or irreversible energy redistribution can take place within dynamical systems that do not possess classical damping properties. Under usual circumstances, energy input to a system returns to its original form after a delay during which the system components undergo oscillatory motions. However, depending on the complexity of the system, the period during which energy travels within the system may become very large, reaching infinity. While conditions that lead to irreversible energy transfer in linear systems are rare, nonlinearities in the system can more readily provide continuous absorption of energy as in the case of thermalized vibrations of atoms. Numerical simulations suggest that the irreversibility attribute for a given system is deeply related to the observation time scale. Examples show that a process may appear reversible when its instantaneous energy time history is observed while its time-average trend exhibits irreversibility. By introducing entropy as a measure of the irreversibility associated with the energy transfer, this presentation suggests three controlling parameters of irreversibility: system complexity as measured by the number of its degrees of freedom, the effect of nonlinearities, and the time-average observation scale. An analysis of their interrelationships discloses new insights into the thermalization phenomenon. [Research sponsored by NSF and INSEAN.]