  A system driven in the vicinity of its critical point by varying a relevant
field in an arbitrary function of time is a generic system that possesses a
long relaxation time compared with the driving time scale and thus represents a
large class of nonequilibrium systems. For such a manifestly nonlinear
nonequilibrium strongly fluctuating system, we show that there exists universal
nonequilibrium critical behavior that is well described incredibly by its
equilibrium critical properties. A dynamic renormalization-group theory is
developed to account for the behavior. The weak driving may give rise to
several time scales depending on its form and thus rich nonequilibrium
phenomena of various regimes and their crossovers, negative susceptibilities,
as well as violation of fluctuation-dissipation theorem. An initial condition
that can be in either equilibrium or nonequilibrium but has longer correlations
than the driving scales also results in a unique regime and complicates the
situation. Implication of the results on measurement is also discussed. The
theory may shed light on study of other nonequilibrium systems and even
nonlinear science.
