The concept of “order” has always been problematic. The revelation here is that there are several scientifically important types of it, and the confusion that this has caused has confused people for a long time.
Ludwig Boltzmann characterized the order that is most commonly associated with entropy. His type of order is Thermal-Kinetic Order. It is essentially the statistically determined proximal separation pattern of particles of an ideal gas in a confining box. When this type of order is lowest, or most disordered, the particles fill the box and are spread out or dissipated maximally. When this type of order is highest, the particles are bunched up in a corner of the box. There are many more ways that particles can be arranged in the disordered state. The ordered states are less likely, and very improbable, and this seems consistent with the notion that this kind of order tends to decrease in isolated systems as their energy level, or temperature, increases, and the particles move around faster, and dissipate.
Contrast Boltzmann’s concept of “order” with the following concept Entropically Functional Order, or simply Functional Order.
Dissipative Structures display entropically functional order, because their structure of flow patterns increases the rate at which energy flows through them. See the post on Dissipative Structures also. This structure is extremely important to the Theory of Levolution, and the mechanism of Thermodynamic Natural Selection, on which it is based. Dissipative Structures form as their energy level is increasing, and their flows adopt the special patterns that make this happen.
Benard cells, swirls at drains, and hurricanes are common examples of dissipative systems, but chemical reaction families, cells, living organisms, and gravitational bodies are examples as well. The latter systems are a special category of dissipative structures called holosystems. Holosystems are dissipative structures that are composed of discrete parts that are also dissipative structures. You and I are holosystems.