Abstract:
The dynamics of a nonequilibrium system can become complex because the system
has many components (e.g., a human brain), because the system is strongly
driven from equilibrium (e.g., large Reynolds-number flows), or because the
system becomes large compared to certain intrinsic length scales. Recent
experimental and theoretical work is reviewed that addresses this last route to
complexity. In the idealized case of a sufficiently large, nontransient,
homogeneous, and chaotic system, the fractal dimension D becomes proportional
to the system's volume V which defines the regime of extensive chaos. The
extensivity of the fractal dimension suggests a new way to characterize
correlations in high-dimensional systems in terms of an intensive dimension
correlation length $\xi_\delta$. Recent calculations at Duke University show
that $\xi_\delta$ is a length scale smaller than and independent of some
commonly used measures of disorder such as the two-point and mutual-information
correlation lengths. Identifying the basic length and time scales of extensive
chaos remains a central problem whose solution will aid the theoretical and
experimental understanding of large nonequilibrium systems.
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