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In this letter we derive exponent inequalities relating the dynamic exponent$z$ to the steady state exponent $\Gamma$ for a general class of stochasticallydriven dynamical systems. We begin by deriving a general exact inequality,relating the response function and the correlation function, from which thevarious exponent inequalities emanate. We then distinguish between two classesof dynamical systems and obtain different and complementary inequalitiesrelating $z$ and $\Gamma$. The consequences of those inequalities for a wideset of dynamical problems, including critical dynamics andKardar-Parisi-Zhang-like problems are discussed.

Exponent Inequalities in Dynamical Systems