I am confused by the concept of disorder as it is used in thermodynamics. I know what disorder looks like in my life: dirty dishes piling up, dust collecting on my shelves. Dust on the shelves may look like disorder to me, but to a house dust mite it looks like habitat, which it may interpret as order. It seems to me that disorder is subjective, what looks like disorder from one perspective, is order when seen from another.

I have encountered the view that increase in entropy is actually the smoothing out of gradients. For example, a heat engine works by using heat as it moves from a hot body to a cold body. It is taking advantage of the smoothing out of a heat gradient. All thermodynamic systems create work by taking advantage of their surroundings sliding down a gradient toward equilibrium. The gradient can be a gradient in heat, electrical potential, chemical potential, or strength of a field.

The way I understand internal entropy is that what really pushes the piston is the difference in temperature between the gas in the cylinder and the gas outside of the cylinder (because efficiency is greater than or equal to 1 - (temp inside the engine/temp of the surroundings)). As the gas expands and pushes the piston it gets colder. Eventually it cools enough that the difference in temperature between the outside and the inside is no longer big enough to push the piston, unless you assume zero friction. So, the way I interpret that is, internal entropy is a matter of context, not an inherent property of the system. This explains why factories are less efficient in the summer when its warm, than they are in the winter when its cold.