Exponent inequalities in dynamical systems

Eytan Katzav, Moshe Schwartz

Research output: Contribution to journalArticlepeer-review


In this Letter, we derive exponent inequalities relating the dynamic exponent z to the steady state exponent Γ for a general class of stochastically driven dynamical systems. We begin by deriving a general exact inequality, relating the response function and the correlation function, from which the various exponent inequalities emanate. We then distinguish between two classes of dynamical systems and obtain different and complementary inequalities relating z and Γ. The consequences of those inequalities for a wide set of dynamical problems, including critical dynamics and Kardar-Parisi-Zhang-like problems, are discussed.

Original languageAmerican English
Article number125701
JournalPhysical Review Letters
Issue number12
StatePublished - 12 Sep 2011

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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