  A stochastic system under the influence of a stochastic environment is
correlated with both present and future states of the environment. Such a
system can be seen as implicitly implementing a predictive model of future
environmental states. The non-predictive model complexity has been shown to
lower-bound the thermodynamic dissipation. Here we explore these statistical
and physical quantities at steady state in simple models. We show that under
quasi-static driving this model complexity saturates the dissipation. Beyond
the quasi-static limit, we demonstrate a lower bound on the ratio of this model
complexity to total dissipation, that is realized in the limit of weak driving.
