There is a tremendous amount of loose talk, even in thermodynamics text books, about bulls in china shops and scrambled eggs in the context of entropy. Both these analogies are misleading because they involve work being done: the bull does work pushing the china through distances and the Delia does work with her fork moving the eggs around the pan.
To Bowdlerize slightly: imagine a metal spring is stretched by a small amount, dx; something it resists with a force F. The thermodynamic identity says, dU = d Work = F.dx (i.e. the small change in the spring's total energy equals the small amount of work that has been done on the spring by stretching it which equals the force times the amount of stretch.)
Interesting oneself again in the spring: this time add energy to the spring in the form of heat, that is touch the spring with something at a higher temperature than T - the temperature of the spring. This adds a small amount of heat energy, d Heat, to the spring. Thus, the thermodynamic identity is: dU = d Heat = T.dS (where dS is the small increase in the entropy of the spring.)
The analogy between the corresponding quantities in the two instances of the identity appears to be utterly fundamental to nature. The spring is pushed through a distance, stretched, by exposing it to a greater force, giving it work energy. Correspondingly the spring is pushed through an entropy by exposing it to a greater temperature, giving it heat energy.
Talk of bulls and china hardly calls attention to temperature difference. Scrambling eggs calls attention to the mixing action of the fork, not temperature.
The appropriate picture to give to a citizen enquiring after entropy is of a fried egg. Here it is clear it is the hot pan which is making the white go white. Error would quickly become apparent if film of an egg being fried were run backward.