Not quite.

Entropy is mathematically equivalent to information content: how much information do I need to describe this system. It can play many roles depending on what that information content is. A fractal is one example of a set with both high structure and high information content. How the information is arranged matters.

Classic example where entropy aligns with disorder:

If we have water in a glass bottle, then we can describe the distribution of both materials using the shape of the bottle (defining where the glass is) and saying that the water is inside and filled to a certain level. We can describe this configuration with a single sentence.

If the bottle falls and breaks, we now have to describe many things. We must consider where the many of pieces of glass went along with each of their unique shapes and sizes; we have to describe where the water splashed and its interactions with the various new forms of matter with which it is in contact: how well it wets each new surface, and how it may have gotten absorbed into any new materials.

When entropy aligns with order:

You. You are an information system. A bundle of structured entropy. You feed your body structured foods (other organisms), and they get broken down via cooking, chewing, digesting and then redistributed. That’s all information increase and entropy increase. Then you turn that chemical energy and entropy into information processing in the brain, mechanical energy in the muscles, and always some waste heat. Each step of the way, you’re increasing entropy. You are a machine that is a ball of structured entropy whose operation increases entropy in a slow and controlled manner. Eventually, if you increase entropy too quickly or too much over time, the structure of your information can break to become digested and processed by the next phase of the circle of life.

Thank you, this is great!