"Systems of any order" in this context probably means any kind of semiotic system, such as language, photography, architecture, etc, whereby something(s) mean(s) something(s). For example, a system whereby some written symbols mean certain physical procedures, or the sound of a bell means food is coming, or some choreography means some sequence of events (e.g. a story told through organized dance). Such a system is considered open if it permits multiple interpretations, and closed if it permits only one interpretation. Examples of open systems might be lyrics, surrealism, or facial expressions. Examples of closed systems might be engineering drawings, traffic signals, or arithmetical operations.
To my knowledge, semiotic openness and closedness have not been rigorously defined. In my opinion, it has been overlooked because semiotics is primarily applied to language and mainstream arts; systems in which interpretants are within the mind. In such a system, perfect closedness is not possible, as absolutely isometric interpretants are not permitted by general relativity; all semiotic systems of this variety consist in non-zero openness, which, in concert with the multitude of axes along which openness can occur (contextual, structural, temporal, etc.), makes the entire notion seem less useful than before. In any case, it's generally sufficient to say that a system is open if a sign's meaning is subject to interpretation, and that a system is closed if its meanings are intended to be the same across the experiences of all human observers, which is to say that all observers of a communication are inspired of a similar interpretant, which is to say that anyone observing a particular sign will perceive the same general meaning.
Openness could be thought of a measure of the ratio of meanings per sign of a sign system; a measure of how many things any particular sign (e.g. written phrase, taken action, motion in the heavens, etc) in a system means. For example, hazard symbology is intended to be a functionally closed system, such that all humans who observe a representamin (e.g. a sign) of a skull with crossed bones are thereby inspired of one interpretant: proximity to a lethal hazard. Meanwhile, Salvador Dali's works and Mona Lisa's expression demonstrate extreme semiotic openness.
A more interesting example is the process of medical research becoming clinical practice. Presently, not all illnesses are readily identifiable, which is to say that the fine details of the semiotic system are not fully known, which is to say that we have not yet modelled a simulacrum of the transformation from presentation of symptoms to identified illness across humans. In still other words, we do not yet always know precisely what presentation means precisely what illness. Yet many sciences work tirelessly to improve this capability, and, as we improve, the process of refining precisely which presentations mean what ailment is a process of seeking a meaning-to-sign ratio of one; seeking closure as a system.
I hope that I've managed to answer your question and provide sufficient examples for validation. Meanwhile, your thoughts on a characteristic difference between the two seems interesting, although I'm not entirely certain I'm understanding correctly. I'd be glad to hear further explanation of your ideas.
