arXiv:2611.13779v1 Announce Type: new Abstract: A great gap in adaptivity, flexibility, and dexterity still exists between intelligent robots, whether they are made of rigid or (partially) compliant components, and their naturally evolved animal and vegetal counterparts. One reason could be of `paradigm' nature. On the one hand, most robots (both rigid and soft) are still designed by following a `Cartesian' approach, with top-down control and a clear mind-body separation. Designing artificial agents on the basis of the principles that we observe in biology is not an easy task. The principles of organization of animals and plants rely on morphological computation and emergence of fit behaviors from loosely coupled networks of embodied agents. Modeling and control require radically new approaches. In this paper we briefly recall and explain some seminal mathematical results linking information metrics and dynamics of the agents, already published years ago; we integrate them with some recent methods developed by us and by the community, we highlight some brief remarks about their relevance and we hint to our current and near future work towards finding concrete and efficient ways for the modeling and control of completely or partially compliant artificial agents and for a better understanding of physical intelligence in nature. We present a technical note summarizing phase-space volume calculations for inverted-pendulum and passive-dynamic walking models, following our proposed framework. Starting from the McGeer compass gait, we introduce knee-ankle compliance, foot-rocker effects, and a Ruina-style compass gait with distributed leg inertia. Standard heel-strike maps are derived and used in the estimation of viable phase-space volumes $W(\gamma)$, based on a state-dependent Monte-Carlo and Reproducing Kernel Hilbert Spaces methods. We show how the methods based on RKHS allow deeper and more subtle analysis.