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Recent bio-mimetic robotics and embodied intelligence research have revealed the importance of reciprocal and dynamical coupling between the brain (controller), the body, and the environment. A typical example of this is a soft robot that has a diversity of compliant and elastic body dynamics. Coupling between the environment and the controller is expected to be enhanced because of the softness of the robot's body. Accordingly, there exists an increasing demand for a method to quantitatively and effectively characterize such coupling regimes. In this paper, we show that the information theoretic approach can be effectively used for this purpose. By using a simple soft robotic platform inspired by the morphology and the material property of an octopus, for example, we analyzed these characteristics and revealed that, because of the compliant and elastic body dynamics, our soft robotic arm was highly sensitive to environmental change.