Complexity in Physics: The Living State of Matter

Professor Paolo Grigolini

Center for Nonlinear Science, University of North Texas

Abstract

We discuss two paradigmatic examples of physical systems exhibiting emergent properties that require a new wisdom, the blinking quantum dots and the random growth of surfaces. We show that both phenomena are characterized by renewal aging, a property that ought not to be confused with the action of rules changing in time: Renewal aging is rather determined by the lack of equilibrium condition. We show that renewal aging corresponds to individual trajectories with abrupt bursts separated by long quiescence periods, and that, while each burst resets to zero the system’s memory, thereby creating renewal, the non-exponential distribution of quiescence times generates aging. This means that the system’s response to external perturbation depends on the time distance between preparation and perturbation. Although, the response to perturbation cannot be predicted from the traditional prime principles, the assumption of renewal condition allows us to make an exact theoretical prediction. We show that external perturbations have the effect of breaking the renewal aging, and of turning it into a traditional form of memory. On the basis of these results we propose a method of analysis of experimental data that is expected to assess whether a generic system fits fully the condition of renewal aging, or it lives in a state where renewal aging is combined to the traditional forms of memory.