FIGURE 5.1 (a) Swarming schools of fish, (b) swirling storms, and (c) galaxies are all examples of systems formed and evolving far from equilibrium. SOURCES: (a) Department of the Interior. (b) Laboratory for Atmospheres, National Aeronautics and Space Administration. (c) National Space Science Data Center, National Aeronautics and Space Administration.

equilibrium conditions also significantly alter the behavior of ordinary fluids and solids. Dramatic examples occur when fluid flow turns turbulent or when solids give way and fracture (Figure 5.2). Both turbulence and fracture generate patterns of amazing complexity that not only completely change the materials properties but also redistribute energy across a whole hierarchy of nested structures, ranging from the microscopic to the macroscopic scale. Far-from-equilibrium processes span a similarly immense range of timescales, from electronic transitions at the subnanosecond scale, to glassy relaxation too slow to measure with any technique, to the age of the universe.

Far-from-equilibrium behavior is not confined to special conditions or certain types of materials. Instead, it arises across the entire spectrum of condensed-matter and materials physics in a host of problems of fundamental interest. Far-from-equilibrium phenomena also benefit and plague us in technology and in everyday life. Indeed, some of the most complex outcomes of behavior far from equilibrium



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