Dynamics and changing environments in highly optimized tolerance

Highly optimized tolerance (HOT) is a mechanism for power laws in complex s ystems based on the robust design of systems in uncertain environments. Onc e the system, the environment, and the optimization scheme have been specif ied, the HOT state is fixed and corresponds to the set of measure zero (typ ically a single point) in the configuration space which minimizes a cost fu nction U. Here we explore the U-dependent structures in configuration space which are associated with departures from the optimal state. We introduce dynamics, quantified by an effective temperature T, such that T=0 correspon ds to the original HOT state, while T-->infinity corresponds to completely random configurations. More generally, T defines the range in state space o ver which fluctuations are likely to be observed. In a fixed environment fl uctuations always raise the average cost. However, in a time-dependent envi ronment, mobile configurations can lower the average U because they adjust more efficiently to changes.