While there is tremendous interest in sustainability, a fundamental theory of sustainability does not exist. We present our efforts at constructing a theory from Information Theory and Ecological Models. We discuss the state of complex systems that incorporate ecological and other components in terms of dynamic behavior in a phase space defined by the system state variables. From sampling the system trajectory, a distribution function for the probability of observing the system in a given state is constructed, and an expression for the Fisher information is derived. Fisher information is the maximum amount of information available from a set of observations. in this case, states of the system. Fisher information is a function of the variability of the observations such that low variability leads to high Fisher information and high variability leads to low Fisher information. Systems in stable dynamic states have constant Fisher information. Systems losing organization migrate toward higher variability and lose Fisher information. Self-organizing systems decrease their variability and acquire Fisher information. These considerations lead us to propose a sustainability hypothesis: "sustainable systems do not lose or gain Fisher information over time." We illustrate these concepts using simulated ecological systems in stable and unstable states, and we discuss the underlying dynamics.