Complexity Explorer Santa Fe Institute

Introduction to Information Theory

Markus Eymann

31 Jan 2026 6:54pm UTC

1

in Introduction to Information Theory

What is disorder?

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.

Sahil Ali

01 Feb 2026 5pm UTC

in Introduction to Information Theory

Hey, let's take a human body. It is biologically speaking a very complex system. What is a disorder in the human body? Isn't it when the body is not doing its proper functions? So, can we say that disorder is a disruption in the operations of organized complexity? Here, the word organized seems very important.

When we talk about physical systems in general, then those are systems of unorganized complexity, billion of gas molecules in a box have no inherent pattern or relationship to each other, they work as a complex system by the definition that there are emergent properties like pressure or temperature. So the entropy in those systems is the averaging out of those aggregates, like you say, " sliding down a gradient towards equilibrium".

But still entropy of a system is not a fixed hard measure. It depends on the type of system we are talking about. For example, entropy in a human brain is simply fuzziness or mental fog. So yeah, entropy or disorder can't be discussed independently or generalized; it needs the context of its particular system.