Nature versus Nurture in Complex and Not-So-Complex Systems

Understanding the dynamical behavior of many-particle systems both in and out of equilibrium is a central issue in both statistical mechanics and complex systems theory. One question involves "nature versus nurture": given a system with a random initial state evolving through a well-defined stochastic dynamics, how much of the information contained in the state at future times depends on the initial condition ("nature") and how much on the dynamical realization ("nurture")? We discuss this question and present both old and new results for low-dimensional Ising spin systems.