Are complexity and disorder correlated in entropy? I am coming from the musical field, but I am looking into the topic of entropy.
In many articles from the field of physics, I keep finding what I consider a sort of misunderstanding, but I may be wrong and would like to ask you to help me understand what I am missing.
In articles like (this), the authors report that "In a closed system, entropy and complexity increase together initially, in other words the greater the disorder the more difficult it is to describe the system."
Similarly, in the same sentence, to an increase in entropy corresponds an increase of disorder. But are complexity and disorder really correlated?
To me, this association sounds very complicated to understand. Somehow, the term "complexity" suggests the "difficulty to describe a closed system" rather then the "complexity of the system itself". Hypothetically considering a completely disordered system, such system may indeed be difficult to describe but that doesn't really mean that it's a complex system, as there may be no relations at all among parts of such system.
In a way, a completely disordered system looks to me as the epitome of simplicity rather than of complexity. For example, the world is a "complex system" where ordered patterns came to emerge from a disordered state describing the beginning of the universe. The same notion of "Complex system" (on Wikipedia) is defined as something difficult to describe because full of components and relations, not because it is disordered.
What am I doing wrong in interpreting the term "complexity". Is there a standard in the field?

Edit: I add some information related to the answers received so far. So far, the answers generally agree that an increase in entropy means that the system is more difficult to describe, which means it is more "complex" and it contains more information.
However, in this answer, exactly the opposite is suggested: an increase in entropy means a loss of information about the system.
 A: Here is another take which might be helpful.
Entropy has at least two different manifestations: one in the realm of thermodynamics and another in the realm of information theory (where it is called Shannon entropy). A system which is highly ordered and regular requires less information to completely describe than one which is completely disordered, where the individual state of each of its constituents has to be specified in detail. So we can state that the information content of a highly-ordered, "uncomplicated" system is low whereas in the case of a completely random system (which will be extremely complicated) it is high, and then assert that an ordered system posses low entropy and a disordered system is in a high entropy state.
A: Of the 3 concepts you mention, the one to drop off the discussion is "disorder". While there are cases where it can be useful, it more often than not is simply a shorthand for much clearer concepts such "number of possible arrangements" (of, for instance, molecules), which tend to be much more helpful.
Entropy is best understood via the down-to-earth approach of considering micro- and macro-states and going from there. You can check the questions Ambiguity in the definition of entropy, Clear up confusion about the meaning of entropy, Entropy definition, additivity, laws in different ensembles, Why can the entropy of an isolated system increase?, among others, or even consult the relevant Wikipedia entry. Statistical mechanics is a topic that takes some getting used to for most people, so don't get disheartened by early difficulties.
As for complexity, you can take a look at the question What is the definition of "Complexity" in physics? Is it quantifiable? and also my answer to another question, but the bottom line is that "more is different":

the properties of a complex system as a whole cannot be understood from the study of its individual constituents

As for the paper you cite, I wouldn't necessarily go much by it, since it's not published in a physics journal and to some degree adopts (e-print from ResearchGate) its own definitions of the terms in question.
