  We introduce a class of maximum-entropy states that naturally includes within
it all of the major continuous-time stochastic processes that have been applied
to animal movement, including Brownian motion, Ornstein-Uhlenbeck motion,
integrated Ornstein-Uhlenbeck motion, a recently discovered hybrid of the
previous models, and a new model that describes central-place foraging. We are
also able to predict a further hierarchy of new models that will emerge as data
quality improves to better resolve the underlying continuity of animal
movement. Finally, we also show that Langevin equations must obey a
fluctuation-dissipation theorem to generate processes that fall from this class
of maximum-entropy distributions.
