Let's consider two situations:
a) A solid metal box (not hollow) where some heat is put on its left side. After some time, the heat will have moved to the right and also have spread out throughout the box.
b) A fully charged battery is connected to a motor and to the motor is a long massive rod attached in the direction of the axis of rotation of the rotor. All these objects are in a container (hollow this time, but not important for the story). The motor and battery lay together at the left side of the container. The rod goes from the rotor all the way to the right side of the container. The rod and rotor are not rotating at first. Then, the motor is turned on and energy starts "flowing" from the battery into the rod and thereby converting electrical enrgy into rotational energy. This goes on until all energy from the battery is put into the rod's rotation.
In both situations no energy is able to escape to the environment, thus both are isolated systems. In my eyes, energy flows from left to right in both cases. I know that when a mass moves from one place to another by pushing itself off of the container, it obbeys Newton's laws of motion and thus causing displacement of the mass and the container.
My question is, is there in any situation displacement of the systems/containers due to energy "flowing" (to the right or left)?