Is the entropy of a rotating body largest when the axis of rotation passes through it's centre of mass? I am looking for an answer to the observation that a body always rotates about its centre of mass when freely tossed. It can be explained if the entropy is highest in the case when the axis passes through the com, however, I am unable to prove it.
I am doing this to be able to visualise the motion of a body in space, when struck tangentially.
 A: This is easily explained by Newton's second law. If there is no net force applied to a body then the center of mass will not accelerate. it will either be stationary or move in a straight line. The only allowed motion is a rotation about the center of mass.
Changes in entropy, arise from the exchange of energy at some temperature and has nothing to do with the mechanics of rotational motion.
A: This question is based on the false premise that an object has a unique axis of rotation. One can choose any point, whether inside, on, or outside the object, as the center of rotation. Pick some other point that is not on the resulting axis of rotation and you'll get another axis passing through that point that is parallel to the original axis of rotation.
The reason that the center of mass is oftentimes used to describe the motion of an object in space is because the Newton-Euler equations of motion become much more complex when the key point of interest is not the center of mass.
When multiple bodies are connected via joints at specific locations, it is oftentimes preferable, despite the added complexity, to use the full-blown Newton-Euler equations (or their Hamiltonian or Lagrangian equivalents) because doing so makes representations the constraints inherent to those joints feasible. The modeling of a robotic arm rarely uses a center of mass formulation.
